LMFDB - Embedded newform 931.2.v.a.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(177,931)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("931.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.v (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			263.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	931.263
Dual form			931.2.v.a.177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 + 2.49362i) q^{2} +(0.113341 - 0.642788i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(-1.26604 + 0.460802i) q^{5} +(1.55303 + 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(2.41875 + 0.880352i) q^{9} +O(q^{10})$	\(q+(-0.439693 + 2.49362i) q^{2} +(0.113341 - 0.642788i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(-1.26604 + 0.460802i) q^{5} +(1.55303 + 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(2.41875 + 0.880352i) q^{9} +(-0.592396 - 3.35965i) q^{10} +(0.592396 + 1.02606i) q^{11} +(-1.43969 + 2.49362i) q^{12} +(2.55303 + 0.929228i) q^{13} +(0.152704 + 0.866025i) q^{15} +(5.08512 + 4.26692i) q^{16} +(3.64543 - 1.32683i) q^{17} +(-3.25877 + 5.64436i) q^{18} +(4.11721 - 1.43128i) q^{19} +5.94356 q^{20} +(-2.81908 + 1.02606i) q^{22} +(-3.87939 + 3.25519i) q^{23} +(-3.05303 - 2.56180i) q^{24} +(-2.43969 + 2.04715i) q^{25} +(-3.43969 + 5.95772i) q^{26} +(1.81908 - 3.15074i) q^{27} +(-3.56418 + 2.99070i) q^{29} -2.22668 q^{30} +3.83750 q^{31} +(-3.52094 + 2.95442i) q^{32} +(0.726682 - 0.264490i) q^{33} +(1.70574 + 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} +(2.05303 + 3.55596i) q^{37} +(1.75877 + 10.8961i) q^{38} +(0.886659 - 1.53574i) q^{39} +(-1.42855 + 8.10170i) q^{40} +(-9.38326 + 3.41523i) q^{41} +(-1.51114 + 8.57013i) q^{43} +(-0.907604 - 5.14728i) q^{44} -3.46791 q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.539363 + 0.196312i) q^{47} +(3.31908 - 2.78504i) q^{48} +(-4.03209 - 6.98378i) q^{50} +(-0.439693 - 2.49362i) q^{51} +(-9.18139 - 7.70410i) q^{52} +(-2.76604 - 1.00676i) q^{53} +(7.05690 + 5.92145i) q^{54} +(-1.22281 - 1.02606i) q^{55} +(-0.453363 - 2.80872i) q^{57} +(-5.89053 - 10.2027i) q^{58} +(-3.69846 + 1.34613i) q^{59} +(0.673648 - 3.82045i) q^{60} +(3.46064 - 2.90382i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(0.819078 + 1.41868i) q^{64} -3.66044 q^{65} +(0.340022 + 1.92836i) q^{66} +(-0.674992 - 3.82807i) q^{67} -17.1138 q^{68} +(1.65270 + 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(12.0398 - 10.1026i) q^{72} +(-1.06418 + 6.03525i) q^{73} +(-9.76991 + 3.55596i) q^{74} +(1.03936 + 1.80023i) q^{75} +(-19.2271 - 0.278817i) q^{76} +(3.43969 + 2.88624i) q^{78} +(7.51367 + 6.30472i) q^{79} +(-8.40420 - 3.05888i) q^{80} +(4.09627 + 3.43718i) q^{81} +(-4.39053 - 24.8999i) q^{82} +(6.15910 + 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(-20.7062 - 7.53644i) q^{86} +(1.51842 + 2.62998i) q^{87} +7.23442 q^{88} +(0.421274 + 2.38917i) q^{89} +(1.52481 - 8.64766i) q^{90} +(20.9932 - 7.64090i) q^{92} +(0.434945 - 2.46669i) q^{93} +(-0.726682 + 1.25865i) q^{94} +(-4.55303 + 3.70929i) q^{95} +(1.50000 + 2.59808i) q^{96} +(-5.64543 - 4.73708i) q^{97} +(0.529563 + 3.00330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9} - 3 q^{12} + 3 q^{13} + 3 q^{15} + 9 q^{16} + 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} - 12 q^{23} - 6 q^{24} - 9 q^{25} - 15 q^{26} - 6 q^{27} - 3 q^{29} + 18 q^{31} - 18 q^{32} - 9 q^{33} - 24 q^{36} - 12 q^{38} + 12 q^{39} - 9 q^{40} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 30 q^{45} - 18 q^{46} + 12 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{54} - 18 q^{55} + 24 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} + 24 q^{65} - 18 q^{66} + 6 q^{67} - 30 q^{68} + 12 q^{69} - 6 q^{71} + 15 q^{72} + 12 q^{73} - 30 q^{74} + 15 q^{75} - 36 q^{76} + 15 q^{78} + 24 q^{79} - 12 q^{80} - 3 q^{81} - 9 q^{82} - 48 q^{86} + 21 q^{87} - 18 q^{88} - 15 q^{89} - 18 q^{90} + 42 q^{92} - 36 q^{93} + 9 q^{94} - 15 q^{95} + 9 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9 - 3 * q^12 + 3 * q^13 + 3 * q^15 + 9 * q^16 + 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 - 12 * q^23 - 6 * q^24 - 9 * q^25 - 15 * q^26 - 6 * q^27 - 3 * q^29 + 18 * q^31 - 18 * q^32 - 9 * q^33 - 24 * q^36 - 12 * q^38 + 12 * q^39 - 9 * q^40 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 30 * q^45 - 18 * q^46 + 12 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^54 - 18 * q^55 + 24 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 + 24 * q^65 - 18 * q^66 + 6 * q^67 - 30 * q^68 + 12 * q^69 - 6 * q^71 + 15 * q^72 + 12 * q^73 - 30 * q^74 + 15 * q^75 - 36 * q^76 + 15 * q^78 + 24 * q^79 - 12 * q^80 - 3 * q^81 - 9 * q^82 - 48 * q^86 + 21 * q^87 - 18 * q^88 - 15 * q^89 - 18 * q^90 + 42 * q^92 - 36 * q^93 + 9 * q^94 - 15 * q^95 + 9 * q^96 - 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.439693	+	2.49362i	−0.310910	+	1.76326i	0.283383	+	0.959007i	$0.408543\pi$
$2$	−0.439693	+	2.49362i	−0.310910	+	1.76326i	−0.594292	+	0.804249i	$0.702568\pi$
$3$	0.113341	−	0.642788i	0.0654373	−	0.371114i	−0.934450	−	0.356095i	$-0.884108\pi$
$3$	0.113341	−	0.642788i	0.0654373	−	0.371114i	0.999887	−	0.0150189i	$-0.00478084\pi$
$4$	−4.14543	−	1.50881i	−2.07271	−	0.754407i
$5$	−1.26604	+	0.460802i	−0.566192	+	0.206077i	−0.609226	−	0.792996i	$-0.708520\pi$
$5$	−1.26604	+	0.460802i	−0.566192	+	0.206077i	0.0430339	+	0.999074i	$0.486298\pi$
$6$	1.55303	+	0.565258i	0.634023	+	0.230766i
$7$		0			0
$7$		0			0
$8$	3.05303	−	5.28801i	1.07941	−	1.86959i
$9$	2.41875	+	0.880352i	0.806249	+	0.293451i
$10$	−0.592396	−	3.35965i	−0.187332	−	1.06241i
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	0.941406	−	0.337275i	$-0.109505\pi$
$11$	0.592396	+	1.02606i	0.178614	+	0.309369i	−0.762792	+	0.646644i	$0.776172\pi$
$12$	−1.43969	+	2.49362i	−0.415603	+	0.719846i
$13$	2.55303	+	0.929228i	0.708084	+	0.257722i	0.670859	−	0.741585i	$-0.265926\pi$
$13$	2.55303	+	0.929228i	0.708084	+	0.257722i	0.0372256	+	0.999307i	$0.488148\pi$
$14$		0			0
$15$	0.152704	+	0.866025i	0.0394279	+	0.223607i
$16$	5.08512	+	4.26692i	1.27128	+	1.06673i
$17$	3.64543	−	1.32683i	0.884147	−	0.321803i	0.140265	−	0.990114i	$-0.455205\pi$
$17$	3.64543	−	1.32683i	0.884147	−	0.321803i	0.743882	+	0.668311i	$0.232982\pi$
$18$	−3.25877	+	5.64436i	−0.768100	+	1.33039i
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$20$	5.94356			1.32902
$21$		0			0
$22$	−2.81908	+	1.02606i	−0.601029	+	0.218757i
$23$	−3.87939	+	3.25519i	−0.808908	+	0.678754i	−0.950347	−	0.311193i	$-0.899272\pi$
$23$	−3.87939	+	3.25519i	−0.808908	+	0.678754i	0.141439	+	0.989947i	$0.454827\pi$
$24$	−3.05303	−	2.56180i	−0.623198	−	0.522925i
$25$	−2.43969	+	2.04715i	−0.487939	+	0.409429i
$26$	−3.43969	+	5.95772i	−0.674579	+	1.16841i
$27$	1.81908	−	3.15074i	0.350082	−	0.606359i
$28$		0			0
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	−0.910641	−	0.413198i	$-0.864412\pi$
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	0.248790	+	0.968557i	$0.419967\pi$
$30$	−2.22668			−0.406535
$31$	3.83750			0.689235			0.344617	−	0.938743i	$-0.388009\pi$
$31$	3.83750			0.689235			0.344617	+	0.938743i	$0.388009\pi$
$32$	−3.52094	+	2.95442i	−0.622421	+	0.522273i
$33$	0.726682	−	0.264490i	0.126499	−	0.0460419i
$34$	1.70574	+	9.67372i	0.292531	+	1.65903i
$35$		0			0
$36$	−8.69846	−	7.29888i	−1.44974	−	1.21648i
$37$	2.05303	+	3.55596i	0.337517	+	0.584596i	0.983965	−	0.178362i	$-0.0570798\pi$
$37$	2.05303	+	3.55596i	0.337517	+	0.584596i	−0.646448	+	0.762958i	$0.723746\pi$
$38$	1.75877	+	10.8961i	0.285310	+	1.76758i
$39$	0.886659	−	1.53574i	0.141979	−	0.245915i
$40$	−1.42855	+	8.10170i	−0.225873	+	1.28099i
$41$	−9.38326	+	3.41523i	−1.46542	+	0.533369i	−0.946852	−	0.321669i	$-0.895756\pi$
$41$	−9.38326	+	3.41523i	−1.46542	+	0.533369i	−0.518566	+	0.855038i	$0.673534\pi$
$42$		0			0
$43$	−1.51114	+	8.57013i	−0.230447	+	1.30693i	0.621545	+	0.783378i	$0.286505\pi$
$43$	−1.51114	+	8.57013i	−0.230447	+	1.30693i	−0.851993	+	0.523554i	$0.824606\pi$
$44$	−0.907604	−	5.14728i	−0.136826	−	0.775981i
$45$	−3.46791			−0.516966
$46$	−6.41147	−	11.1050i	−0.945320	−	1.63734i
$47$	0.539363	+	0.196312i	0.0786742	+	0.0286351i	0.381057	−	0.924551i	$-0.375560\pi$
$47$	0.539363	+	0.196312i	0.0786742	+	0.0286351i	−0.302383	+	0.953186i	$0.597782\pi$
$48$	3.31908	−	2.78504i	0.479068	−	0.401985i
$49$		0			0
$50$	−4.03209	−	6.98378i	−0.570223	−	0.987656i
$51$	−0.439693	−	2.49362i	−0.0615693	−	0.349177i
$52$	−9.18139	−	7.70410i	−1.27323	−	1.06837i
$53$	−2.76604	−	1.00676i	−0.379945	−	0.138289i	0.144985	−	0.989434i	$-0.453687\pi$
$53$	−2.76604	−	1.00676i	−0.379945	−	0.138289i	−0.524931	+	0.851145i	$0.675909\pi$
$54$	7.05690	+	5.92145i	0.960323	+	0.805807i
$55$	−1.22281	−	1.02606i	−0.164884	−	0.138354i
$56$		0			0
$57$	−0.453363	−	2.80872i	−0.0600494	−	0.372023i
$58$	−5.89053	−	10.2027i	−0.773464	−	1.33968i
$59$	−3.69846	+	1.34613i	−0.481499	+	0.175251i	−0.571354	−	0.820704i	$-0.693582\pi$
$59$	−3.69846	+	1.34613i	−0.481499	+	0.175251i	0.0898553	+	0.995955i	$0.471360\pi$
$60$	0.673648	−	3.82045i	0.0869676	−	0.493218i
$61$	3.46064	−	2.90382i	0.443089	−	0.371796i	−0.393775	−	0.919207i	$-0.628831\pi$
$61$	3.46064	−	2.90382i	0.443089	−	0.371796i	0.836864	+	0.547411i	$0.184387\pi$
$62$	−1.68732	+	9.56926i	−0.214290	+	1.21530i
$63$		0			0
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$	−3.66044			−0.454022
$66$	0.340022	+	1.92836i	0.0418539	+	0.237365i
$67$	−0.674992	−	3.82807i	−0.0824634	−	0.467673i	−0.997875	−	0.0651547i	$-0.979246\pi$
$67$	−0.674992	−	3.82807i	−0.0824634	−	0.467673i	0.915412	−	0.402519i	$-0.131865\pi$
$68$	−17.1138			−2.07535
$69$	1.65270	+	2.86257i	0.198962	+	0.344613i
$70$		0			0
$71$	−1.20439	+	6.83045i	−0.142935	+	0.810625i	0.826067	+	0.563572i	$0.190573\pi$
$71$	−1.20439	+	6.83045i	−0.142935	+	0.810625i	−0.969002	+	0.247053i	$0.920538\pi$
$72$	12.0398	−	10.1026i	1.41891	−	1.19060i
$73$	−1.06418	+	6.03525i	−0.124553	+	0.706373i	0.857020	+	0.515283i	$0.172313\pi$
$73$	−1.06418	+	6.03525i	−0.124553	+	0.706373i	−0.981573	+	0.191090i	$0.938798\pi$
$74$	−9.76991	+	3.55596i	−1.13573	+	0.413372i
$75$	1.03936	+	1.80023i	0.120015	+	0.207873i
$76$	−19.2271	−	0.278817i	−2.20551	−	0.0319825i
$77$		0			0
$78$	3.43969	+	2.88624i	0.389468	+	0.326803i
$79$	7.51367	+	6.30472i	0.845354	+	0.709336i	0.958761	−	0.284212i	$-0.0917321\pi$
$79$	7.51367	+	6.30472i	0.845354	+	0.709336i	−0.113407	+	0.993549i	$0.536177\pi$
$80$	−8.40420	−	3.05888i	−0.939618	−	0.341993i
$81$	4.09627	+	3.43718i	0.455141	+	0.381908i
$82$	−4.39053	−	24.8999i	−0.484853	−	2.74974i
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	0.976161	+	0.217047i	$0.0696426\pi$
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	−0.300112	+	0.953904i	$0.597024\pi$
$84$		0			0
$85$	−4.00387	+	3.35965i	−0.434281	+	0.364405i
$86$	−20.7062	−	7.53644i	−2.23281	−	0.812675i
$87$	1.51842	+	2.62998i	0.162792	+	0.281963i
$88$	7.23442			0.771192
$89$	0.421274	+	2.38917i	0.0446550	+	0.253251i	0.998961	−	0.0455813i	$-0.0145140\pi$
$89$	0.421274	+	2.38917i	0.0446550	+	0.253251i	−0.954306	+	0.298832i	$0.903403\pi$
$90$	1.52481	−	8.64766i	0.160730	−	0.911543i
$91$		0			0
$92$	20.9932	−	7.64090i	2.18869	−	0.796619i
$93$	0.434945	−	2.46669i	0.0451017	−	0.255784i
$94$	−0.726682	+	1.25865i	−0.0749515	+	0.129820i
$95$	−4.55303	+	3.70929i	−0.467131	+	0.380565i
$96$	1.50000	+	2.59808i	0.153093	+	0.265165i
$97$	−5.64543	−	4.73708i	−0.573207	−	0.480977i	0.309502	−	0.950899i	$-0.399838\pi$
$97$	−5.64543	−	4.73708i	−0.573207	−	0.480977i	−0.882708	+	0.469922i	$0.844282\pi$
$98$		0			0
$99$	0.529563	+	3.00330i	0.0532231	+	0.301843i
$100$	13.2023	−	4.80526i	1.32023	−	0.480526i
$101$	−1.66250	+	1.39501i	−0.165425	+	0.138808i	−0.721742	−	0.692162i	$-0.756658\pi$
$101$	−1.66250	+	1.39501i	−0.165425	+	0.138808i	0.556317	+	0.830970i	$0.312214\pi$
$102$	6.41147			0.634831
$103$	12.4757			1.22926			0.614631	−	0.788815i	$-0.289305\pi$
$103$	12.4757			1.22926			0.614631	+	0.788815i	$0.289305\pi$
$104$	12.7083	−	10.6635i	1.24615	−	1.04564i
$105$		0			0
$106$	3.72668	−	6.45480i	0.361967	−	0.626946i
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	−0.658191	−	0.752851i	$-0.728678\pi$
$107$	3.34002	−	5.78509i	0.322892	−	0.559266i	0.981083	+	0.193585i	$0.0620116\pi$
$108$	−12.2947	+	10.3165i	−1.18306	+	0.992706i
$109$	7.24170	+	6.07650i	0.693629	+	0.582024i	0.919953	−	0.392028i	$-0.128227\pi$
$109$	7.24170	+	6.07650i	0.693629	+	0.582024i	−0.226324	+	0.974052i	$0.572671\pi$
$110$	3.09627	−	2.59808i	0.295217	−	0.247717i
$111$	2.51842	−	0.916629i	0.239038	−	0.0870026i
$112$		0			0
$113$	1.31046			0.123278			0.0616388	−	0.998099i	$-0.480367\pi$
$113$	1.31046			0.123278			0.0616388	+	0.998099i	$0.480367\pi$
$114$	7.20321	+	0.104455i	0.674643	+	0.00978315i
$115$	3.41147	−	5.90885i	0.318122	−	0.551003i
$116$	19.2875	−	7.02006i	1.79080	−	0.651796i
$117$	5.35710	+	4.49514i	0.495264	+	0.415576i
$118$	−1.73055	−	9.81445i	−0.159310	−	0.903493i
$119$		0			0
$120$	5.04576	+	1.83651i	0.460613	+	0.167649i
$121$	4.79813	−	8.31061i	0.436194	−	0.755510i
$122$	5.71941	+	9.90630i	0.517811	+	0.896875i
$123$	1.13176	+	6.41852i	0.102047	+	0.578739i
$124$	−15.9081	−	5.79006i	−1.42859	−	0.519963i
$125$	5.51367	−	9.54996i	0.493158	−	0.854174i
$126$		0			0
$127$	13.6284	+	4.96032i	1.20932	+	0.440157i	0.866468	−	0.499232i	$-0.166385\pi$
$127$	13.6284	+	4.96032i	1.20932	+	0.440157i	0.342853	+	0.939389i	$0.388607\pi$
$128$	−12.5360	+	4.56272i	−1.10803	+	0.403291i
$129$	5.33750	+	1.94269i	0.469940	+	0.171044i
$130$	1.60947	−	9.12776i	0.141160	−	0.800558i
$131$	3.43969	−	19.5075i	0.300527	−	1.70438i	−0.343318	−	0.939219i	$-0.611551\pi$
$131$	3.43969	−	19.5075i	0.300527	−	1.70438i	0.643845	−	0.765156i	$-0.277338\pi$
$132$	−3.41147			−0.296931
$133$		0			0
$134$	9.84255			0.850267
$135$	−0.851167	+	4.82721i	−0.0732568	+	0.415460i
$136$	4.11334	−	23.3279i	0.352716	−	2.00035i
$137$	−9.58899	−	3.49011i	−0.819243	−	0.298180i	−0.101807	−	0.994804i	$-0.532462\pi$
$137$	−9.58899	−	3.49011i	−0.819243	−	0.298180i	−0.717436	+	0.696624i	$0.754685\pi$
$138$	−7.86484	+	2.86257i	−0.669499	+	0.243678i
$139$	−1.56031	−	0.567905i	−0.132344	−	0.0481691i	0.274999	−	0.961444i	$-0.411322\pi$
$139$	−1.56031	−	0.567905i	−0.132344	−	0.0481691i	−0.407343	+	0.913275i	$0.633545\pi$
$140$		0			0
$141$	0.187319	−	0.324446i	0.0157751	−	0.0273232i
$142$	−16.5030	−	6.00660i	−1.38490	−	0.504063i
$143$	0.558963	+	3.17004i	0.0467429	+	0.265092i
$144$	8.54323	+	14.7973i	0.711936	+	1.23311i
$145$	3.13429	−	5.42874i	0.260288	−	0.450832i
$146$	−14.5817	−	5.30731i	−1.20679	−	0.439236i
$147$		0			0
$148$	−3.14543	−	17.8386i	−0.258553	−	1.46633i
$149$	8.58512	+	7.20377i	0.703321	+	0.590156i	0.922716	−	0.385480i	$-0.125964\pi$
$149$	8.58512	+	7.20377i	0.703321	+	0.590156i	−0.219396	+	0.975636i	$0.570409\pi$
$150$	−4.94609	+	1.80023i	−0.403846	+	0.146988i
$151$	5.52094	−	9.56256i	0.449288	−	0.778190i	−0.549052	−	0.835788i	$-0.685011\pi$
$151$	5.52094	−	9.56256i	0.449288	−	0.778190i	0.998340	+	0.0575986i	$0.0183443\pi$
$152$	5.00134	−	26.1416i	0.405663	−	2.12036i
$153$	9.98545			0.807276
$154$		0			0
$155$	−4.85844	+	1.76833i	−0.390239	+	0.142036i
$156$	−5.99273	+	5.02849i	−0.479802	+	0.402602i
$157$	−8.42127	−	7.06629i	−0.672091	−	0.563951i	0.241593	−	0.970378i	$-0.422330\pi$
$157$	−8.42127	−	7.06629i	−0.672091	−	0.563951i	−0.913683	+	0.406427i	$0.866775\pi$
$158$	−19.0253	+	15.9641i	−1.51357	+	1.27004i
$159$	−0.960637	+	1.66387i	−0.0761835	+	0.131954i
$160$	3.09627	−	5.36289i	0.244781	−	0.423974i
$161$		0			0
$162$	−10.3721	+	8.70323i	−0.814910	+	0.683791i
$163$	−6.33275			−0.496019			−0.248010	−	0.968758i	$-0.579776\pi$
$163$	−6.33275			−0.496019			−0.248010	+	0.968758i	$0.579776\pi$
$164$	44.0506			3.43977
$165$	−0.798133	+	0.669713i	−0.0621346	+	0.0521371i
$166$	−29.3097	+	10.6679i	−2.27488	+	0.827988i
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	0.925770	+	0.378087i	$0.123418\pi$
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	−0.740626	+	0.671917i	$0.765471\pi$
$168$		0			0
$169$	−4.30406	−	3.61154i	−0.331082	−	0.277811i
$170$	−6.61721	−	11.4613i	−0.507517	−	0.879045i
$171$	11.2185	+	0.162683i	0.857902	+	0.0124406i
$172$	19.1951	−	33.2468i	1.46361	−	2.53505i
$173$	−4.38413	+	24.8637i	−0.333319	+	1.89035i	0.109912	+	0.993941i	$0.464943\pi$
$173$	−4.38413	+	24.8637i	−0.333319	+	1.89035i	−0.443231	+	0.896407i	$0.646168\pi$
$174$	−7.22580	+	2.62998i	−0.547787	+	0.199378i
$175$		0			0
$176$	−1.36571	+	7.74535i	−0.102945	+	0.583828i
$177$	0.446089	+	2.52990i	0.0335301	+	0.190159i
$178$	−6.14290			−0.460430
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	0.736264	−	0.676695i	$-0.236588\pi$
$179$	−2.91534	−	5.04952i	−0.217903	−	0.377419i	−0.954167	+	0.299276i	$0.903255\pi$
$180$	14.3760	+	5.23243i	1.07152	+	0.390002i
$181$	−10.3892	+	8.71756i	−0.772222	+	0.647971i	−0.941277	−	0.337635i	$-0.890373\pi$
$181$	−10.3892	+	8.71756i	−0.772222	+	0.647971i	0.169055	+	0.985607i	$0.445928\pi$
$182$		0			0
$183$	−1.47431	−	2.55358i	−0.108984	−	0.188766i
$184$	5.36959	+	30.4524i	0.395851	+	2.24498i
$185$	−4.23783	−	3.55596i	−0.311571	−	0.261439i
$186$	5.95976	+	2.16918i	0.436991	+	0.159052i
$187$	3.52094	+	2.95442i	0.257477	+	0.216049i
$188$	−1.93969	−	1.62760i	−0.141467	−	0.118705i
$189$		0			0
$190$	−7.24763	−	12.9845i	−0.525798	−	0.941994i
$191$	5.14203	+	8.90625i	0.372064	+	0.644434i	0.989883	−	0.141887i	$-0.0453169\pi$
$191$	5.14203	+	8.90625i	0.372064	+	0.644434i	−0.617819	+	0.786320i	$0.711984\pi$
$192$	1.00475	−	0.365698i	0.0725114	−	0.0263920i
$193$	2.39646	−	13.5910i	0.172501	−	0.978301i	−0.768488	−	0.639864i	$-0.778991\pi$
$193$	2.39646	−	13.5910i	0.172501	−	0.978301i	0.940989	−	0.338437i	$-0.109898\pi$
$194$	14.2947	−	11.9947i	1.02630	−	0.861169i
$195$	−0.414878	+	2.35289i	−0.0297100	+	0.168494i
$196$		0			0
$197$	3.97044	+	6.87700i	0.282882	+	0.489966i	0.972093	−	0.234594i	$-0.0753762\pi$
$197$	3.97044	+	6.87700i	0.282882	+	0.489966i	−0.689211	+	0.724560i	$0.742043\pi$
$198$	−7.72193			−0.548774
$199$	−4.69459	−	26.6244i	−0.332791	−	1.88735i	−0.448039	−	0.894014i	$-0.647877\pi$
$199$	−4.69459	−	26.6244i	−0.332791	−	1.88735i	0.115248	−	0.993337i	$-0.463234\pi$
$200$	3.37686	+	19.1511i	0.238780	+	1.35419i
$201$	−2.53714			−0.178956
$202$	−2.74763	−	4.75903i	−0.193322	−	0.334844i
$203$		0			0
$204$	−1.93969	+	11.0005i	−0.135806	+	0.770192i
$205$	10.3059	−	8.64766i	0.719793	−	0.603978i
$206$	−5.48545	+	31.1095i	−0.382190	+	2.16750i
$207$	−12.2490	+	4.45826i	−0.851362	+	0.309871i
$208$	9.01754	+	15.6188i	0.625254	+	1.08297i
$209$	3.90760	+	3.37662i	0.270295	+	0.233566i
$210$		0			0
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	0.404635	−	0.914478i	$-0.367399\pi$
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	−0.830321	+	0.557285i	$0.811843\pi$
$212$	9.94743	+	8.34689i	0.683193	+	0.573267i
$213$	4.25402	+	1.54834i	0.291481	+	0.106090i
$214$	12.9572	+	10.8724i	0.885738	+	0.743223i
$215$	−2.03596	−	11.5465i	−0.138851	−	0.787465i
$216$	−11.1074	−	19.2386i	−0.755764	−	1.30902i
$217$		0			0
$218$	−18.3366	+	15.3863i	−1.24191	+	1.04209i
$219$	3.75877	+	1.36808i	0.253994	+	0.0924463i
$220$	3.52094	+	6.09845i	0.237382	+	0.411158i
$221$	10.5398			0.708986
$222$	1.17840	+	6.68302i	0.0790888	+	0.448535i
$223$	2.68732	−	15.2405i	0.179956	−	1.02058i	−0.752310	−	0.658809i	$-0.771060\pi$
$223$	2.68732	−	15.2405i	0.179956	−	1.02058i	0.932266	−	0.361773i	$-0.117828\pi$
$224$		0			0
$225$	−7.70321	+	2.80374i	−0.513547	+	0.186916i
$226$	−0.576199	+	3.26779i	−0.0383282	+	0.217370i
$227$	4.93629	−	8.54990i	0.327633	−	0.567477i	−0.654409	−	0.756141i	$-0.727082\pi$
$227$	4.93629	−	8.54990i	0.327633	−	0.567477i	0.982042	+	0.188664i	$0.0604157\pi$
$228$	−2.35844	+	12.3274i	−0.156192	+	0.816400i
$229$	10.0594	+	17.4234i	0.664746	+	1.15137i	0.979354	+	0.202152i	$0.0647935\pi$
$229$	10.0594	+	17.4234i	0.664746	+	1.15137i	−0.314608	+	0.949222i	$0.601873\pi$
$230$	13.2344	+	11.1050i	0.872652	+	0.732242i
$231$		0			0
$232$	4.93330	+	27.9781i	0.323887	+	1.83685i
$233$	−3.32160	+	1.20897i	−0.217606	+	0.0792019i	−0.448523	−	0.893772i	$-0.648050\pi$
$233$	−3.32160	+	1.20897i	−0.217606	+	0.0792019i	0.230917	+	0.972973i	$0.425827\pi$
$234$	−13.5646	+	11.3821i	−0.886749	+	0.744070i
$235$	−0.773318			−0.0504457
$236$	17.3628			1.13022
$237$	4.90420	−	4.11511i	0.318562	−	0.267305i
$238$		0			0
$239$	−5.98680	+	10.3694i	−0.387254	+	0.670743i	−0.992079	−	0.125615i	$-0.959910\pi$
$239$	−5.98680	+	10.3694i	−0.387254	+	0.670743i	0.604825	+	0.796358i	$0.293243\pi$
$240$	−2.91875	+	5.05542i	−0.188404	+	0.326326i
$241$	−9.88326	+	8.29304i	−0.636636	+	0.534201i	−0.902983	−	0.429676i	$-0.858628\pi$
$241$	−9.88326	+	8.29304i	−0.636636	+	0.534201i	0.266347	+	0.963877i	$0.414183\pi$
$242$	18.6138	+	15.6188i	1.19654	+	1.00402i
$243$	11.0346	−	9.25914i	0.707871	−	0.593974i
$244$	−18.7271	+	6.81612i	−1.19888	+	0.436358i
$245$		0			0
$246$	−16.5030			−1.05219
$247$	11.8414	+	0.171714i	0.753448	+	0.0109259i
$248$	11.7160	−	20.2927i	0.743967	−	1.28859i
$249$	7.55525	−	2.74989i	0.478795	−	0.174267i
$250$	21.3897	+	17.9480i	1.35280	+	1.13513i
$251$	−2.49407	−	14.1446i	−0.157424	−	0.892798i	−0.956536	−	0.291615i	$-0.905807\pi$
$251$	−2.49407	−	14.1446i	−0.157424	−	0.892798i	0.799112	−	0.601183i	$-0.205304\pi$
$252$		0			0
$253$	−5.63816	−	2.05212i	−0.354468	−	0.129016i
$254$	−18.3614	+	31.8029i	−1.15210	+	1.99549i
$255$	1.70574	+	2.95442i	0.106817	+	0.185013i
$256$	−5.29679	−	30.0396i	−0.331049	−	1.87747i
$257$	4.67752	+	1.70248i	0.291776	+	0.106198i	0.483761	−	0.875200i	$-0.339270\pi$
$257$	4.67752	+	1.70248i	0.291776	+	0.106198i	−0.191985	+	0.981398i	$0.561493\pi$
$258$	−7.19119	+	12.4555i	−0.447704	+	0.775446i
$259$		0			0
$260$	15.1741	+	5.52293i	0.941059	+	0.342517i
$261$	−11.2537	+	4.09602i	−0.696588	+	0.253537i
$262$	47.1318	+	17.1546i	2.91181	+	1.05981i
$263$	−4.17499	+	23.6776i	−0.257441	+	1.46002i	0.532287	+	0.846564i	$0.321333\pi$
$263$	−4.17499	+	23.6776i	−0.257441	+	1.46002i	−0.789728	+	0.613457i	$0.789778\pi$
$264$	0.819955	−	4.65020i	0.0504648	−	0.286200i
$265$	3.96585			0.243620
$266$		0			0
$267$	1.58347			0.0969070
$268$	−2.97771	+	16.8874i	−0.181893	+	1.03156i
$269$	2.27672	−	12.9119i	0.138814	−	0.787254i	−0.833313	−	0.552801i	$-0.813559\pi$
$269$	2.27672	−	12.9119i	0.138814	−	0.787254i	0.972127	−	0.234453i	$-0.0753300\pi$
$270$	−11.6630	−	4.24497i	−0.709786	−	0.258341i
$271$	−24.9675	+	9.08743i	−1.51667	+	0.552022i	−0.960313	−	0.278923i	$-0.910022\pi$
$271$	−24.9675	+	9.08743i	−1.51667	+	0.552022i	−0.556354	+	0.830945i	$0.687800\pi$
$272$	24.1989	+	8.80769i	1.46728	+	0.534045i
$273$		0			0
$274$	12.9192	−	22.3767i	0.780478	−	1.35183i
$275$	−3.54576	−	1.29055i	−0.213817	−	0.0778231i
$276$	−2.53209	−	14.3602i	−0.152414	−	0.864382i
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	0.999989	−	0.00459317i	$-0.00146206\pi$
$277$	8.25537	+	14.2987i	0.496017	+	0.859127i	−0.503973	+	0.863720i	$0.668129\pi$
$278$	2.10220	−	3.64111i	0.126081	−	0.218379i
$279$	9.28194	+	3.37835i	0.555695	+	0.202256i
$280$		0			0
$281$	−3.36706	−	19.0955i	−0.200862	−	1.13914i	−0.903820	−	0.427913i	$-0.859249\pi$
$281$	−3.36706	−	19.0955i	−0.200862	−	1.13914i	0.702958	−	0.711231i	$-0.251862\pi$
$282$	0.726682	+	0.609758i	0.0432733	+	0.0363106i
$283$	−10.6284	+	3.86841i	−0.631790	+	0.229953i	−0.638010	−	0.770028i	$-0.720242\pi$
$283$	−10.6284	+	3.86841i	−0.631790	+	0.229953i	0.00622012	+	0.999981i	$0.498020\pi$
$284$	15.2986	−	26.4980i	0.907805	−	1.57236i
$285$	1.86824	+	3.34705i	0.110665	+	0.198262i
$286$	−8.15064			−0.481958
$287$		0			0
$288$	−11.1172	+	4.04633i	−0.655088	+	0.238433i
$289$	−1.49407	+	1.25367i	−0.0878865	+	0.0737455i
$290$	12.1591	+	10.2027i	0.714007	+	0.599123i
$291$	−3.68479	+	3.09191i	−0.216006	+	0.181251i
$292$	13.5175	−	23.4131i	0.791054	−	1.37015i
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	−0.803445	−	0.595379i	$-0.797002\pi$
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	0.917336	+	0.398115i	$0.130335\pi$
$294$		0			0
$295$	4.06212	−	3.40852i	0.236506	−	0.198452i
$296$	25.0719			1.45728
$297$	4.31046			0.250118
$298$	−21.7383	+	18.2406i	−1.25927	+	1.05665i
$299$	−12.9290	+	4.70578i	−0.747704	+	0.272142i
$300$	−1.59240	−	9.03093i	−0.0919370	−	0.521401i
$301$		0			0
$302$	21.4179	+	17.9717i	1.23246	+	1.03416i
$303$	0.708263	+	1.22675i	0.0406887	+	0.0704748i
$304$	27.0437	+	10.2896i	1.55106	+	0.590148i
$305$	−3.04323	+	5.27103i	−0.174255	+	0.301819i
$306$	−4.39053	+	24.8999i	−0.250990	+	1.42343i
$307$	21.7777	−	7.92642i	1.24292	−	0.452385i	0.364914	−	0.931041i	$-0.381098\pi$
$307$	21.7777	−	7.92642i	1.24292	−	0.452385i	0.878002	+	0.478657i	$0.158876\pi$
$308$		0			0
$309$	1.41400	−	8.01919i	0.0804397	−	0.456196i
$310$	−2.27332	−	12.8926i	−0.129116	−	0.732252i
$311$	3.46110			0.196261			0.0981306	−	0.995174i	$-0.468714\pi$
$311$	3.46110			0.196261			0.0981306	+	0.995174i	$0.468714\pi$
$312$	−5.41400	−	9.37732i	−0.306507	−	0.530886i
$313$	−21.5094	−	7.82878i	−1.21578	−	0.442509i	−0.347077	−	0.937837i	$-0.612826\pi$
$313$	−21.5094	−	7.82878i	−1.21578	−	0.442509i	−0.868706	+	0.495328i	$0.835048\pi$
$314$	21.3234	−	17.8925i	1.20335	−	1.00973i
$315$		0			0
$316$	−21.6348	−	37.4725i	−1.21705	−	2.10799i
$317$	4.53580	+	25.7238i	0.254756	+	1.44479i	0.796699	+	0.604376i	$0.206578\pi$
$317$	4.53580	+	25.7238i	0.254756	+	1.44479i	−0.541943	+	0.840415i	$0.682311\pi$
$318$	−3.72668	−	3.12706i	−0.208982	−	0.175357i
$319$	−5.18004	−	1.88538i	−0.290027	−	0.105561i
$320$	−1.69072	−	1.41868i	−0.0945143	−	0.0793069i
$321$	−3.34002	−	2.80261i	−0.186422	−	0.156427i
$322$		0			0
$323$	13.1099	−	10.6805i	0.729456	−	0.594277i
$324$	−11.7947	−	20.4291i	−0.655263	−	1.13495i
$325$	−8.13088	+	2.95940i	−0.451020	+	0.164158i
$326$	2.78446	−	15.7915i	0.154217	−	0.874609i
$327$	4.72668	−	3.96616i	0.261386	−	0.219329i
$328$	−10.5876	+	60.0455i	−0.584605	+	3.31546i
$329$		0			0
$330$	−1.31908	−	2.28471i	−0.0726128	−	0.125769i
$331$	19.0446			1.04678			0.523392	−	0.852092i	$-0.324666\pi$
$331$	19.0446			1.04678			0.523392	+	0.852092i	$0.324666\pi$
$332$	−9.43629	−	53.5159i	−0.517884	−	2.93706i
$333$	1.83527	+	10.4084i	0.100572	+	0.570375i
$334$	−34.8881			−1.90899
$335$	2.61856	+	4.53547i	0.143067	+	0.247799i
$336$		0			0
$337$	0.295445	−	1.67555i	0.0160939	−	0.0912731i	−0.975703	−	0.219098i	$-0.929688\pi$
$337$	0.295445	−	1.67555i	0.0160939	−	0.0912731i	0.991797	+	0.127825i	$0.0407996\pi$
$338$	10.8983	−	9.14473i	0.592788	−	0.497408i
$339$	0.148529	−	0.842347i	0.00806696	−	0.0457500i
$340$	21.6668	−	7.88609i	1.17505	−	0.427683i
$341$	2.27332	+	3.93750i	0.123107	+	0.213228i
$342$	−5.33837	+	27.9032i	−0.288666	+	1.50883i
$343$		0			0
$344$	40.7053	+	34.1558i	2.19468	+	1.84156i
$345$	−3.41147	−	2.86257i	−0.183668	−	0.154115i
$346$	−60.0729	−	21.8647i	−3.22954	−	1.17546i
$347$	−3.75490	−	3.15074i	−0.201574	−	0.169140i	0.536413	−	0.843956i	$-0.319779\pi$
$347$	−3.75490	−	3.15074i	−0.201574	−	0.169140i	−0.737987	+	0.674815i	$0.764223\pi$
$348$	−2.32635	−	13.1934i	−0.124706	−	0.707240i
$349$	−14.0646	−	24.3607i	−0.752863	−	1.30400i	−0.946430	−	0.322910i	$-0.895339\pi$
$349$	−14.0646	−	24.3607i	−0.752863	−	1.30400i	0.193566	−	0.981087i	$-0.437994\pi$
$350$		0			0
$351$	7.57192	−	6.35359i	0.404159	−	0.339130i
$352$	−5.11721	−	1.86251i	−0.272748	−	0.0992723i
$353$	−4.15998	−	7.20529i	−0.221413	−	0.383499i	0.733824	−	0.679340i	$-0.237734\pi$
$353$	−4.15998	−	7.20529i	−0.221413	−	0.383499i	−0.955237	+	0.295841i	$0.904400\pi$
$354$	−6.50475			−0.345723
$355$	−1.62267	−	9.20264i	−0.0861226	−	0.488426i
$356$	1.85844	−	10.5397i	0.0984972	−	0.558605i
$357$		0			0
$358$	13.8735	−	5.04952i	0.733235	−	0.266876i
$359$	4.32888	−	24.5503i	0.228469	−	1.29571i	−0.627471	−	0.778640i	$-0.715910\pi$
$359$	4.32888	−	24.5503i	0.228469	−	1.29571i	0.855940	−	0.517075i	$-0.172979\pi$
$360$	−10.5876	+	18.3383i	−0.558018	+	0.966516i
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$	−17.1702	−	29.7397i	−0.902448	−	1.56309i
$363$	−4.79813	−	4.02611i	−0.251837	−	0.211316i
$364$		0			0
$365$	−1.43376	−	8.13127i	−0.0750466	−	0.425610i
$366$	7.01589	−	2.55358i	0.366727	−	0.133478i
$367$	1.98087	−	1.66214i	0.103400	−	0.0867632i	−0.589622	−	0.807679i	$-0.700723\pi$
$367$	1.98087	−	1.66214i	0.103400	−	0.0867632i	0.693022	+	0.720916i	$0.256279\pi$
$368$	−33.6168			−1.75240
$369$	−25.7023			−1.33801
$370$	10.7306	−	9.00400i	0.557855	−	0.468096i
$371$		0			0
$372$	−5.52481	+	9.56926i	−0.286448	+	0.496143i
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	−0.386622	−	0.922238i	$-0.626358\pi$
$373$	11.6917	−	20.2505i	0.605371	−	1.04853i	0.991993	−	0.126295i	$-0.0403086\pi$
$374$	−8.91534	+	7.48086i	−0.461001	+	0.386826i
$375$	−5.51367	−	4.62652i	−0.284725	−	0.238912i
$376$	2.68479	−	2.25281i	0.138458	−	0.116180i
$377$	−11.8785	+	4.32342i	−0.611774	+	0.222668i
$378$		0			0
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$	24.4709	−	8.50692i	1.25533	−	0.436396i
$381$	4.73308	−	8.19793i	0.242483	−	0.419993i
$382$	−24.4697	+	8.90625i	−1.25198	+	0.455683i
$383$	21.0514	+	17.6643i	1.07568	+	0.902601i	0.995555	−	0.0941836i	$-0.0300241\pi$
$383$	21.0514	+	17.6643i	1.07568	+	0.902601i	0.0801235	+	0.996785i	$0.474469\pi$
$384$	1.51202	+	8.57510i	0.0771600	+	0.437596i
$385$		0			0
$386$	32.8371	+	11.9517i	1.67136	+	0.608327i
$387$	−11.1998	+	19.3986i	−0.569318	+	0.986088i
$388$	16.2554	+	28.1551i	0.825241	+	1.42936i
$389$	−0.580375	−	3.29147i	−0.0294262	−	0.166884i	0.966553	−	0.256466i	$-0.0825581\pi$
$389$	−0.580375	−	3.29147i	−0.0294262	−	0.166884i	−0.995979	+	0.0895817i	$0.971447\pi$
$390$	−5.68479	−	2.06910i	−0.287861	−	0.104773i
$391$	−9.82295	+	17.0138i	−0.496768	+	0.860427i
$392$		0			0
$393$	−12.1493	−	4.42198i	−0.612851	−	0.223060i
$394$	−18.8944	+	6.87700i	−0.951886	+	0.346458i
$395$	−12.4179	−	4.51974i	−0.624811	−	0.227413i
$396$	2.33615	−	13.2490i	0.117396	−	0.665786i
$397$	2.27884	−	12.9239i	0.114372	−	0.648633i	−0.872688	−	0.488279i	$-0.837625\pi$
$397$	2.27884	−	12.9239i	0.114372	−	0.648633i	0.987059	−	0.160355i	$-0.0512639\pi$
$398$	68.4552			3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	2.97178	−	16.8538i	0.148404	−	0.841639i	−0.816167	−	0.577816i	$-0.803905\pi$
$401$	2.97178	−	16.8538i	0.148404	−	0.841639i	0.964571	−	0.263823i	$-0.0849836\pi$
$402$	1.11556	−	6.32667i	0.0556392	−	0.315546i
$403$	9.79726	+	3.56591i	0.488036	+	0.177631i
$404$	8.99660	−	3.27449i	0.447597	−	0.162912i
$405$	−6.76991	−	2.46405i	−0.336400	−	0.122440i
$406$		0			0
$407$	−2.43242	+	4.21307i	−0.120571	+	0.208834i
$408$	−14.5287	−	5.28801i	−0.719277	−	0.261795i
$409$	1.52775	+	8.66431i	0.0755425	+	0.428423i	0.999000	+	0.0447208i	$0.0142398\pi$
$409$	1.52775	+	8.66431i	0.0755425	+	0.428423i	−0.923457	+	0.383702i	$0.874649\pi$
$410$	17.0326	+	29.5013i	0.841178	+	1.45696i
$411$	−3.33022	+	5.76811i	−0.164268	+	0.284520i
$412$	−51.7169	−	18.8234i	−2.54791	−	0.927364i
$413$		0			0
$414$	−5.73143	−	32.5046i	−0.281684	−	1.59751i
$415$	−12.7135	−	10.6679i	−0.624080	−	0.523665i
$416$	−11.7344	+	4.27098i	−0.575327	+	0.209402i
$417$	−0.541889	+	0.938579i	−0.0265364	+	0.0459624i
$418$	−10.1382	+	8.25941i	−0.495873	+	0.403981i
$419$	−6.84018			−0.334165			−0.167082	−	0.985943i	$-0.553435\pi$
$419$	−6.84018			−0.334165			−0.167082	+	0.985943i	$0.553435\pi$
$420$		0			0
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	−0.229210	−	0.973377i	$-0.573614\pi$
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	0.450090	+	0.892983i	$0.351392\pi$
$422$	15.6570	−	13.1378i	0.762173	−	0.639539i
$423$	1.13176	+	0.949659i	0.0550280	+	0.0461740i
$424$	−13.7686	+	11.5532i	−0.668661	+	0.561073i
$425$	−6.17752	+	10.6998i	−0.299654	+	0.519015i
$426$	−5.73143	+	9.92713i	−0.277689	+	0.480971i
$427$		0			0
$428$	−22.5744	+	18.9422i	−1.09118	+	0.915606i
$429$	2.10101			0.101438
$430$	29.6878			1.43167
$431$	0.998656	−	0.837972i	0.0481036	−	0.0403637i	−0.618419	−	0.785849i	$-0.712226\pi$
$431$	0.998656	−	0.837972i	0.0481036	−	0.0403637i	0.666522	+	0.745485i	$0.267782\pi$
$432$	22.6942	−	8.26001i	1.09187	−	0.397410i
$433$	−3.44238	−	19.5227i	−0.165430	−	0.938202i	−0.948620	−	0.316419i	$-0.897520\pi$
$433$	−3.44238	−	19.5227i	−0.165430	−	0.938202i	0.783189	−	0.621783i	$-0.213591\pi$
$434$		0			0
$435$	−3.13429	−	2.62998i	−0.150277	−	0.126098i
$436$	−20.8516	−	36.1161i	−0.998612	−	1.72965i
$437$	−11.3131	+	18.9548i	−0.541181	+	0.906731i
$438$	−5.06418	+	8.77141i	−0.241976	+	0.419114i
$439$	6.00253	−	34.0420i	0.286485	−	1.62474i	−0.413448	−	0.910528i	$-0.635676\pi$
$439$	6.00253	−	34.0420i	0.286485	−	1.62474i	0.699933	−	0.714209i	$-0.253213\pi$
$440$	−9.15910	+	3.33364i	−0.436643	+	0.158925i
$441$		0			0
$442$	−4.63429	+	26.2823i	−0.220430	+	1.25012i
$443$	2.95377	+	16.7517i	0.140338	+	0.795896i	0.970993	+	0.239109i	$0.0768552\pi$
$443$	2.95377	+	16.7517i	0.140338	+	0.795896i	−0.830655	+	0.556788i	$0.812034\pi$
$444$	−11.8229			−0.561092
$445$	−1.63429	−	2.83067i	−0.0774726	−	0.134186i
$446$	36.8225	+	13.4023i	1.74360	+	0.634618i
$447$	5.60354	−	4.70193i	0.265038	−	0.222394i
$448$		0			0
$449$	−18.7049	−	32.3978i	−0.882737	−	1.52895i	−0.848286	−	0.529539i	$-0.822365\pi$
$449$	−18.7049	−	32.3978i	−0.882737	−	1.52895i	−0.0344512	−	0.999406i	$-0.510968\pi$
$450$	−3.60442	−	20.4417i	−0.169914	−	0.963630i
$451$	−9.06283	−	7.60462i	−0.426752	−	0.358088i
$452$	−5.43242	−	1.97724i	−0.255519	−	0.0930015i
$453$	−5.52094	−	4.63262i	−0.259397	−	0.217660i
$454$	19.1498	+	16.0686i	0.898743	+	0.754135i
$455$		0			0
$456$	−16.2366	−	6.17771i	−0.760351	−	0.289298i
$457$	−4.55556	−	7.89046i	−0.213100	−	0.369100i	0.739583	−	0.673065i	$-0.235023\pi$
$457$	−4.55556	−	7.89046i	−0.213100	−	0.369100i	−0.952683	+	0.303965i	$0.901689\pi$
$458$	−47.8705	+	17.4234i	−2.23684	+	0.814144i
$459$	2.45084	−	13.8994i	0.114395	−	0.648768i
$460$	−23.0574	+	19.3474i	−1.07506	+	0.902079i
$461$	4.24540	−	24.0769i	0.197728	−	1.12137i	−0.710751	−	0.703443i	$-0.751645\pi$
$461$	4.24540	−	24.0769i	0.197728	−	1.12137i	0.908480	−	0.417929i	$-0.137244\pi$
$462$		0			0
$463$	0.125362	+	0.217134i	0.00582609	+	0.0100911i	0.868924	−	0.494946i	$-0.164812\pi$
$463$	0.125362	+	0.217134i	0.00582609	+	0.0100911i	−0.863098	+	0.505037i	$0.831479\pi$
$464$	−30.8854			−1.43382
$465$	0.586000	+	3.32337i	0.0271751	+	0.154118i
$466$	−1.55422	−	8.81439i	−0.0719976	−	0.408319i
$467$	−15.3618			−0.710861			−0.355431	−	0.934703i	$-0.615666\pi$
$467$	−15.3618			−0.710861			−0.355431	+	0.934703i	$0.615666\pi$
$468$	−15.4251	−	26.7171i	−0.713028	−	1.23500i
$469$		0			0
$470$	0.340022	−	1.92836i	0.0156841	−	0.0889487i
$471$	−5.49660	+	4.61219i	−0.253270	+	0.212519i
$472$	−4.17318	+	23.6673i	−0.192086	+	1.08938i
$473$	−9.68866	+	3.52638i	−0.445485	+	0.162143i
$474$	8.10519	+	14.0386i	0.372284	+	0.644814i
$475$	−7.11468	+	11.9204i	−0.326444	+	0.546946i
$476$		0			0
$477$	−5.80406	−	4.87019i	−0.265750	−	0.222991i
$478$	−23.2251	−	19.4882i	−1.06229	−	0.891368i
$479$	−0.675870	−	0.245996i	−0.0308813	−	0.0112399i	0.326533	−	0.945186i	$-0.394119\pi$
$479$	−0.675870	−	0.245996i	−0.0308813	−	0.0112399i	−0.357415	+	0.933946i	$0.616342\pi$
$480$	−3.09627	−	2.59808i	−0.141325	−	0.118585i
$481$	1.93717	+	10.9862i	0.0883272	+	0.500928i
$482$	−16.3341	−	28.2915i	−0.743998	−	1.28864i
$483$		0			0
$484$	−32.4295	+	27.2116i	−1.47407	+	1.23689i
$485$	9.33022	+	3.39592i	0.423664	+	0.154201i
$486$	18.2369	+	31.5873i	0.827245	+	1.43283i
$487$	11.7469			0.532303			0.266152	−	0.963931i	$-0.414248\pi$
$487$	11.7469			0.532303			0.266152	+	0.963931i	$0.414248\pi$
$488$	−4.78998	−	27.1653i	−0.216832	−	1.22972i
$489$	−0.717759	+	4.07061i	−0.0324582	+	0.184079i
$490$		0			0
$491$	−0.0834734	+	0.0303818i	−0.00376710	+	0.00137111i	−0.343903	−	0.939005i	$-0.611749\pi$
$491$	−0.0834734	+	0.0303818i	−0.00376710	+	0.00137111i	0.340136	+	0.940376i	$0.389527\pi$
$492$	4.99273	−	28.3152i	0.225089	−	1.27655i
$493$	−9.02481	+	15.6314i	−0.406457	+	0.704005i
$494$	−5.63475	+	29.4524i	−0.253519	+	1.32513i
$495$	−2.05438	−	3.55829i	−0.0923374	−	0.159933i
$496$	19.5141	+	16.3743i	0.876211	+	0.735228i
$497$		0			0
$498$	3.53519	+	20.0490i	0.158416	+	0.898419i
$499$	−13.8045	+	5.02444i	−0.617976	+	0.224925i	−0.631989	−	0.774977i	$-0.717761\pi$
$499$	−13.8045	+	5.02444i	−0.617976	+	0.224925i	0.0140137	+	0.999902i	$0.495539\pi$
$500$	−37.2656	+	31.2696i	−1.66657	+	1.39842i
$501$	8.99319			0.401786
$502$	36.3678			1.62318
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	−0.555183	−	0.831728i	$-0.687352\pi$
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	0.722686	+	0.691176i	$0.242907\pi$
$504$		0			0
$505$	1.46198	−	2.53223i	0.0650573	−	0.112683i
$506$	7.59627	−	13.1571i	0.337695	−	0.584905i
$507$	−2.80928	+	2.35726i	−0.124764	+	0.104690i
$508$	−49.0112	−	41.1253i	−2.17452	−	1.82464i
$509$	−4.91329	+	4.12274i	−0.217778	+	0.182737i	−0.745149	−	0.666897i	$-0.767622\pi$
$509$	−4.91329	+	4.12274i	−0.217778	+	0.182737i	0.527372	+	0.849635i	$0.323177\pi$
$510$	−8.11721	+	2.95442i	−0.359436	+	0.130824i
$511$		0			0
$512$	50.5553			2.23425
$513$	2.97993	−	15.5759i	0.131567	−	0.687691i
$514$	−6.30200	+	10.9154i	−0.277969	+	0.481457i
$515$	−15.7947	+	5.74881i	−0.695999	+	0.253323i
$516$	−19.1951	−	16.1066i	−0.845015	−	0.709052i
$517$	0.118089	+	0.669713i	0.00519353	+	0.0294540i
$518$		0			0
$519$	15.4851	+	5.63613i	0.679723	+	0.247399i
$520$	−11.1755	+	19.3565i	−0.490076	+	0.848837i
$521$	−17.9067	−	31.0154i	−0.784508	−	1.35881i	−0.929293	−	0.369344i	$-0.879582\pi$
$521$	−17.9067	−	31.0154i	−0.784508	−	1.35881i	0.144785	−	0.989463i	$-0.453751\pi$
$522$	−5.26574	−	29.8635i	−0.230475	−	1.30709i
$523$	36.4342	+	13.2610i	1.59316	+	0.579862i	0.978011	−	0.208551i	$-0.0668748\pi$
$523$	36.4342	+	13.2610i	1.59316	+	0.579862i	0.615146	+	0.788413i	$0.289097\pi$
$524$	−43.6921	+	75.6770i	−1.90870	+	3.30596i
$525$		0			0
$526$	−57.2071	−	20.8217i	−2.49435	−	0.907869i
$527$	13.9893	−	5.09170i	0.609384	−	0.221798i
$528$	4.82383	+	1.75573i	0.209930	+	0.0764083i
$529$	0.459455	−	2.60570i	0.0199763	−	0.113291i
$530$	−1.74376	+	9.88933i	−0.0757439	+	0.429565i
$531$	−10.1307			−0.439636
$532$		0			0
$533$	−27.1293			−1.17510
$534$	−0.696242	+	3.94858i	−0.0301293	+	0.170872i
$535$	−1.56283	+	8.86327i	−0.0675672	+	0.383193i
$536$	−22.3037	−	8.11787i	−0.963371	−	0.350638i
$537$	−3.57620	+	1.30163i	−0.154324	+	0.0561695i
$538$	31.1964	+	11.3546i	1.34497	+	0.489530i
$539$		0			0
$540$	10.8118	−	18.7266i	0.465266	−	0.805864i
$541$	−8.91787	−	3.24584i	−0.383409	−	0.139550i	0.143123	−	0.989705i	$-0.454286\pi$
$541$	−8.91787	−	3.24584i	−0.383409	−	0.139550i	−0.526532	+	0.850155i	$0.676508\pi$
$542$	−11.6826	−	66.2552i	−0.501809	−	2.84590i
$543$	4.42602	+	7.66610i	0.189939	+	0.328984i
$544$	−8.91534	+	15.4418i	−0.382242	+	0.662063i
$545$	−11.9684	−	4.35613i	−0.512669	−	0.186596i
$546$		0			0
$547$	2.46791	+	13.9962i	0.105520	+	0.598435i	0.991011	+	0.133779i	$0.0427111\pi$
$547$	2.46791	+	13.9962i	0.105520	+	0.598435i	−0.885491	+	0.464657i	$0.846178\pi$
$548$	34.4846	+	28.9360i	1.47311	+	1.23608i
$549$	10.9268	−	3.97703i	0.466344	−	0.169735i
$550$	4.77719	−	8.27433i	0.203700	−	0.352819i
$551$	−10.3939	+	17.4147i	−0.442796	+	0.741891i
$552$	20.1830			0.859047
$553$		0			0
$554$	−39.2854	+	14.2987i	−1.66908	+	0.607494i
$555$	−2.76604	+	2.32099i	−0.117412	+	0.0985204i
$556$	5.61128	+	4.70842i	0.237971	+	0.199682i
$557$	17.2665	−	14.4883i	0.731606	−	0.613890i	−0.198963	−	0.980007i	$-0.563757\pi$
$557$	17.2665	−	14.4883i	0.731606	−	0.613890i	0.930569	+	0.366117i	$0.119313\pi$
$558$	−12.5055	+	21.6602i	−0.529401	+	0.916949i
$559$	−11.8216	+	20.4756i	−0.500001	+	0.866026i
$560$		0			0
$561$	2.29813	−	1.92836i	0.0970273	−	0.0814155i
$562$	49.0975			2.07105
$563$	42.9718			1.81105			0.905524	−	0.424296i	$-0.139478\pi$
$563$	42.9718			1.81105			0.905524	+	0.424296i	$0.139478\pi$
$564$	−1.26604	+	1.06234i	−0.0533101	+	0.0447325i
$565$	−1.65910	+	0.603863i	−0.0697989	+	0.0254047i
$566$	−4.97313	−	28.2040i	−0.209036	−	1.18550i
$567$		0			0
$568$	32.4424	+	27.2224i	1.36125	+	1.14223i
$569$	−3.71348	−	6.43193i	−0.155677	−	0.269641i	0.777628	−	0.628724i	$-0.216423\pi$
$569$	−3.71348	−	6.43193i	−0.155677	−	0.269641i	−0.933305	+	0.359084i	$0.883089\pi$
$570$	−9.16772	+	3.18701i	−0.383993	+	0.133489i
$571$	−2.02229	+	3.50271i	−0.0846301	+	0.146584i	−0.905234	−	0.424914i	$-0.860304\pi$
$571$	−2.02229	+	3.50271i	−0.0846301	+	0.146584i	0.820603	+	0.571498i	$0.193638\pi$
$572$	2.46585	−	13.9845i	0.103102	−	0.584723i
$573$	6.30763	−	2.29579i	0.263505	−	0.0959080i
$574$		0			0
$575$	2.80066	−	15.8833i	0.116796	−	0.662381i
$576$	0.732201	+	4.15252i	0.0305084	+	0.173022i
$577$	−3.23442			−0.134651			−0.0673254	−	0.997731i	$-0.521447\pi$
$577$	−3.23442			−0.134651			−0.0673254	+	0.997731i	$0.521447\pi$
$578$	−2.46926	−	4.27688i	−0.102707	−	0.177895i
$579$	−8.46451	−	3.08083i	−0.351773	−	0.128035i
$580$	−21.1839	+	17.7754i	−0.879614	+	0.738084i
$581$		0			0
$582$	−6.08987	−	10.5480i	−0.252433	−	0.437227i
$583$	−0.605600	−	3.43453i	−0.0250814	−	0.142244i
$584$	28.6655	+	24.0532i	1.18619	+	0.995329i
$585$	−8.85369	−	3.22248i	−0.366055	−	0.133233i
$586$	7.56283	+	6.34597i	0.312418	+	0.262150i
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.991738	+	0.128279i	$0.0409452\pi$
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.298543	+	0.954396i	$0.403499\pi$
$588$		0			0
$589$	15.7998	−	5.49254i	0.651019	−	0.226316i
$590$	6.71348	+	11.6281i	0.276390	+	0.478721i
$591$	4.87046	−	1.77270i	0.200344	−	0.0729193i
$592$	−4.73308	+	26.8426i	−0.194528	+	1.10322i
$593$	8.47565	−	7.11192i	0.348053	−	0.292051i	−0.451955	−	0.892041i	$-0.649273\pi$
$593$	8.47565	−	7.11192i	0.348053	−	0.292051i	0.800008	+	0.599990i	$0.204829\pi$
$594$	−1.89528	+	10.7487i	−0.0777642	+	0.441023i
$595$		0			0
$596$	−24.7199	−	42.8161i	−1.01257	−	1.75381i
$597$	−17.6459			−0.722198
$598$	−6.04963	−	34.3092i	−0.247388	−	1.40301i
$599$	−7.73736	−	43.8807i	−0.316140	−	1.79292i	−0.565755	−	0.824573i	$-0.691415\pi$
$599$	−7.73736	−	43.8807i	−0.316140	−	1.79292i	0.249615	−	0.968345i	$-0.419696\pi$
$600$	12.6928			0.518183
$601$	−2.49953	−	4.32932i	−0.101958	−	0.176597i	0.810533	−	0.585693i	$-0.199177\pi$
$601$	−2.49953	−	4.32932i	−0.101958	−	0.176597i	−0.912491	+	0.409096i	$0.865844\pi$
$602$		0			0
$603$	1.73742	−	9.85337i	0.0707530	−	0.401260i
$604$	−37.3148	+	31.3108i	−1.51832	+	1.27402i
$605$	−2.24510	+	12.7326i	−0.0912763	+	0.517654i
$606$	−3.37046	+	1.22675i	−0.136916	+	0.0498332i
$607$	−15.5940	−	27.0097i	−0.632943	−	1.09629i	−0.986947	−	0.161045i	$-0.948514\pi$
$607$	−15.5940	−	27.0097i	−0.632943	−	1.09629i	0.354004	−	0.935244i	$-0.384820\pi$
$608$	−10.2679	+	17.2035i	−0.416417	+	0.697692i
$609$		0			0
$610$	−11.8059	−	9.90630i	−0.478006	−	0.401095i
$611$	1.19459	+	1.00238i	0.0483280	+	0.0405520i
$612$	−41.3940	−	15.0662i	−1.67325	−	0.609014i
$613$	12.5398	+	10.5222i	0.506479	+	0.424986i	0.859888	−	0.510483i	$-0.170533\pi$
$613$	12.5398	+	10.5222i	0.506479	+	0.424986i	−0.353409	+	0.935469i	$0.614978\pi$
$614$	10.1900	+	57.7904i	0.411235	+	2.33223i
$615$	−4.39053	−	7.60462i	−0.177043	−	0.306648i
$616$		0			0
$617$	12.3014	−	10.3221i	0.495235	−	0.415551i	−0.360663	−	0.932696i	$-0.617450\pi$
$617$	12.3014	−	10.3221i	0.495235	−	0.415551i	0.855898	+	0.517145i	$0.173005\pi$
$618$	19.3751	+	7.05196i	0.779381	+	0.283671i
$619$	11.9213	+	20.6483i	0.479156	+	0.829923i	0.999714	−	0.0239031i	$-0.00760931\pi$
$619$	11.9213	+	20.6483i	0.479156	+	0.829923i	−0.520558	+	0.853826i	$0.674276\pi$
$620$	22.8084			0.916007
$621$	3.19934	+	18.1444i	0.128385	+	0.728108i
$622$	−1.52182	+	8.63068i	−0.0610195	+	0.346059i
$623$		0			0
$624$	11.0617	−	4.02611i	0.442820	−	0.161173i
$625$	0.185259	−	1.05066i	0.00741037	−	0.0420263i
$626$	28.9795	−	50.1940i	1.15825	−	2.00616i
$627$	2.61334	−	2.12905i	0.104367	−	0.0850261i
$628$	24.2481	+	41.9989i	0.967604	+	1.67594i
$629$	12.2023	+	10.2390i	0.486539	+	0.408255i
$630$		0			0
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	0.964541	+	0.263931i	$0.0850193\pi$
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	−0.816103	+	0.577907i	$0.803870\pi$
$632$	56.2789	−	20.4838i	2.23865	−	0.814803i
$633$	−4.03596	+	3.38657i	−0.160415	+	0.134604i
$634$	−66.1397			−2.62674
$635$	−19.5398			−0.775414
$636$	6.49273	−	5.44804i	0.257453	−	0.216029i
$637$		0			0
$638$	6.97906	−	12.0881i	0.276303	−	0.478572i
$639$	−8.92633	+	15.4609i	−0.353120	+	0.611622i
$640$	13.7686	−	11.5532i	0.544251	−	0.456680i
$641$	9.76991	+	8.19793i	0.385888	+	0.323799i	0.815009	−	0.579448i	$-0.196732\pi$
$641$	9.76991	+	8.19793i	0.385888	+	0.323799i	−0.429120	+	0.903247i	$0.641176\pi$
$642$	8.45723	−	7.09646i	0.333780	−	0.280075i
$643$	26.8828	−	9.78456i	1.06016	−	0.385865i	0.247669	−	0.968845i	$-0.420335\pi$
$643$	26.8828	−	9.78456i	1.06016	−	0.385865i	0.812487	+	0.582979i	$0.198113\pi$
$644$		0			0
$645$	−7.65270			−0.301325
$646$	20.8687	+	37.3873i	0.821068	+	1.47099i
$647$	8.35638	−	14.4737i	0.328523	−	0.569019i	−0.653696	−	0.756757i	$-0.726782\pi$
$647$	8.35638	−	14.4737i	0.328523	−	0.569019i	0.982219	+	0.187738i	$0.0601157\pi$
$648$	30.6819	−	11.1673i	1.20530	−	0.438692i
$649$	−3.57217	−	2.99740i	−0.140220	−	0.117658i
$650$	−3.80453	−	21.5766i	−0.149226	−	0.846302i
$651$		0			0
$652$	26.2520	+	9.55493i	1.02811	+	0.374200i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	7.81180	+	13.5304i	0.305466	+	0.529082i
$655$	4.63429	+	26.2823i	0.181077	+	1.02694i
$656$	−62.2875	−	22.6708i	−2.43192	−	0.885146i
$657$	−7.88713	+	13.6609i	−0.307706	+	0.532963i
$658$		0			0
$659$	41.2533	+	15.0150i	1.60700	+	0.584900i	0.980844	−	0.194797i	$-0.0624047\pi$
$659$	41.2533	+	15.0150i	1.60700	+	0.584900i	0.626157	+	0.779697i	$0.284627\pi$
$660$	4.31908	−	1.57202i	0.168120	−	0.0611906i
$661$	−10.1074	−	3.67880i	−0.393133	−	0.143089i	0.137887	−	0.990448i	$-0.455969\pi$
$661$	−10.1074	−	3.67880i	−0.393133	−	0.143089i	−0.531020	+	0.847359i	$0.678191\pi$
$662$	−8.37376	+	47.4900i	−0.325455	+	1.84575i
$663$	1.19459	−	6.77487i	0.0463941	−	0.263114i
$664$	75.2158			2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	4.09152	−	23.2042i	0.158424	−	0.898469i
$668$	10.5548	−	59.8595i	0.408379	−	2.31603i
$669$	−9.49185	−	3.45475i	−0.366976	−	0.133568i
$670$	−12.4611	+	4.53547i	−0.481414	+	0.175221i
$671$	5.02956	+	1.83061i	0.194164	+	0.0706700i
$672$		0			0
$673$	−2.32888	+	4.03374i	−0.0897717	+	0.155489i	−0.907415	−	0.420237i	$-0.861947\pi$
$673$	−2.32888	+	4.03374i	−0.0897717	+	0.155489i	0.817643	+	0.575726i	$0.195280\pi$
$674$	4.04829	+	1.47346i	0.155934	+	0.0567554i
$675$	2.01202	+	11.4107i	0.0774428	+	0.439200i
$676$	12.3931	+	21.4654i	0.476656	+	0.825592i
$677$	1.63429	−	2.83067i	0.0628107	−	0.108791i	−0.832910	−	0.553408i	$-0.813327\pi$
$677$	1.63429	−	2.83067i	0.0628107	−	0.108791i	0.895721	+	0.444617i	$0.146660\pi$
$678$	2.03519	+	0.740748i	0.0781609	+	0.0284482i
$679$		0			0
$680$	5.54189	+	31.4296i	0.212522	+	1.20527i
$681$	−4.93629	−	4.14204i	−0.189159	−	0.158723i
$682$	−10.8182	+	3.93750i	−0.414250	+	0.150775i
$683$	−3.10947	+	5.38576i	−0.118981	+	0.206080i	−0.919364	−	0.393408i	$-0.871296\pi$
$683$	−3.10947	+	5.38576i	−0.118981	+	0.206080i	0.800383	+	0.599488i	$0.204629\pi$
$684$	−46.2602	−	17.6011i	−1.76880	−	0.672993i
$685$	13.7483			0.525297
$686$		0			0
$687$	12.3397	−	4.49129i	0.470790	−	0.171353i
$688$	−44.2524	+	37.1322i	−1.68711	+	1.41565i
$689$	−6.12630	−	5.14057i	−0.233393	−	0.195840i
$690$	8.63816	−	7.24827i	0.328849	−	0.275937i
$691$	11.1088	−	19.2409i	0.422597	−	0.731959i	−0.573596	−	0.819139i	$-0.694452\pi$
$691$	11.1088	−	19.2409i	0.422597	−	0.731959i	0.996193	+	0.0871792i	$0.0277853\pi$
$692$	55.6887	−	96.4557i	2.11697	−	3.66670i
$693$		0			0
$694$	9.50774	−	7.97794i	0.360909	−	0.302839i
$695$	2.23711			0.0848584
$696$	18.5431			0.702875
$697$	−29.6746	+	24.8999i	−1.12400	+	0.943152i
$698$	66.9304	−	24.3607i	2.53335	−	0.922065i
$699$	0.400634	+	2.27211i	0.0151534	+	0.0859391i
$700$		0			0
$701$	−21.2750	−	17.8518i	−0.803544	−	0.674254i	0.145513	−	0.989356i	$-0.453517\pi$
$701$	−21.2750	−	17.8518i	−0.803544	−	0.674254i	−0.949058	+	0.315102i	$0.897961\pi$
$702$	12.5141	+	21.6751i	0.472316	+	0.818075i
$703$	13.5424	+	11.7022i	0.510760	+	0.441355i
$704$	−0.970437	+	1.68085i	−0.0365747	+	0.0633493i
$705$	−0.0876485	+	0.497079i	−0.00330103	+	0.0187211i
$706$	19.7964	−	7.20529i	0.745047	−	0.271175i
$707$		0			0
$708$	1.96791	−	11.1606i	0.0739586	−	0.419440i
$709$	−1.06061	−	6.01503i	−0.0398321	−	0.225899i	0.958393	−	0.285452i	$-0.0921437\pi$
$709$	−1.06061	−	6.01503i	−0.0398321	−	0.225899i	−0.998225	+	0.0595527i	$0.981033\pi$
$710$	23.6614			0.887996
$711$	12.6233	+	21.8642i	0.473411	+	0.819972i
$712$	13.9201	+	5.06650i	0.521678	+	0.189875i
$713$	−14.8871	+	12.4918i	−0.557527	+	0.467821i
$714$		0			0
$715$	−2.16843	−	3.75584i	−0.0810948	−	0.140460i
$716$	4.46657	+	25.3312i	0.166923	+	0.946670i
$717$	5.98680	+	5.02352i	0.223581	+	0.187607i
$718$	59.3157	+	21.5892i	2.21364	+	0.805700i
$719$	−29.6642	−	24.8912i	−1.10629	−	0.928284i	−0.108455	−	0.994101i	$-0.534590\pi$
$719$	−29.6642	−	24.8912i	−1.10629	−	0.928284i	−0.997832	+	0.0658171i	$0.979035\pi$
$720$	−17.6348	−	14.7973i	−0.657208	−	0.551463i
$721$		0			0
$722$	22.8366	+	42.3442i	0.849891	+	1.57589i
$723$	4.21048	+	7.29277i	0.156590	+	0.271221i
$724$	56.2208	−	20.4627i	2.08943	−	0.760490i
$725$	2.57310	−	14.5928i	0.0955626	−	0.541962i
$726$	12.1493	−	10.1945i	0.450903	−	0.378352i
$727$	1.92366	−	10.9096i	0.0713445	−	0.404615i	−0.928132	−	0.372252i	$-0.878586\pi$
$727$	1.92366	−	10.9096i	0.0713445	−	0.404615i	0.999476	−	0.0323628i	$-0.0103032\pi$
$728$		0			0
$729$	3.31996	+	5.75033i	0.122961	+	0.212975i
$730$	20.9067			0.773793
$731$	5.86231	+	33.2468i	0.216825	+	1.22968i
$732$	2.25877	+	12.8101i	0.0834866	+	0.473476i
$733$	15.8075			0.583862			0.291931	−	0.956439i	$-0.405702\pi$
$733$	15.8075			0.583862			0.291931	+	0.956439i	$0.405702\pi$
$734$	3.27379	+	5.67036i	0.120838	+	0.209297i
$735$		0			0
$736$	4.04189	−	22.9227i	0.148986	−	0.844942i
$737$	3.52797	−	2.96032i	0.129954	−	0.109045i
$738$	11.3011	−	64.0919i	0.416000	−	2.35925i
$739$	−1.45589	+	0.529900i	−0.0535558	+	0.0194927i	−0.368659	−	0.929565i	$-0.620183\pi$
$739$	−1.45589	+	0.529900i	−0.0535558	+	0.0194927i	0.315103	+	0.949057i	$0.397961\pi$
$740$	12.2023	+	21.1351i	0.448567	+	0.776940i
$741$	1.45249	−	7.59202i	0.0533584	−	0.278900i
$742$		0			0
$743$	29.2349	+	24.5310i	1.07252	+	0.899955i	0.995279	−	0.0970576i	$-0.0309431\pi$
$743$	29.2349	+	24.5310i	1.07252	+	0.899955i	0.0772453	+	0.997012i	$0.475388\pi$
$744$	−11.7160	−	9.83089i	−0.429530	−	0.360418i
$745$	−14.1887	−	5.16425i	−0.519832	−	0.189204i
$746$	45.3564	+	38.0586i	1.66062	+	1.39342i
$747$	5.50582	+	31.2251i	0.201448	+	1.14247i
$748$	−10.1382	−	17.5598i	−0.370688	−	0.642050i
$749$		0			0
$750$	13.9611	−	11.7148i	0.509787	−	0.427762i
$751$	23.8195	+	8.66961i	0.869188	+	0.316358i	0.737838	−	0.674978i	$-0.235847\pi$
$751$	23.8195	+	8.66961i	0.869188	+	0.316358i	0.131349	+	0.991336i	$0.458069\pi$
$752$	1.90508	+	3.29969i	0.0694710	+	0.120327i
$753$	−9.37464			−0.341631
$754$	−5.55809	−	31.5215i	−0.202414	−	1.14794i
$755$	−2.58331	+	14.6507i	−0.0940163	+	0.533193i
$756$		0			0
$757$	−39.8153	+	14.4916i	−1.44711	+	0.526705i	−0.941783	−	0.336222i	$-0.890851\pi$
$757$	−39.8153	+	14.4916i	−1.44711	+	0.526705i	−0.505328	+	0.862927i	$0.668628\pi$
$758$	−11.1853	+	63.4348i	−0.406267	+	2.30405i
$759$	−1.95811	+	3.39155i	−0.0710749	+	0.123105i
$760$	5.71419	+	35.4011i	0.207276	+	1.28413i
$761$	−1.42855	−	2.47432i	−0.0517848	−	0.0896940i	0.838971	−	0.544176i	$-0.183158\pi$
$761$	−1.42855	−	2.47432i	−0.0517848	−	0.0896940i	−0.890756	+	0.454482i	$0.849824\pi$
$762$	18.3614	+	15.4071i	0.665165	+	0.558139i
$763$		0			0
$764$	−7.87804	−	44.6786i	−0.285018	−	1.61641i
$765$	−12.6420	+	4.60132i	−0.457073	+	0.166361i
$766$	−53.3041	+	44.7275i	−1.92596	+	1.61607i
$767$	−10.6932			−0.386108
$768$	−19.9094			−0.718419
$769$	−14.6472	+	12.2905i	−0.528193	+	0.443207i	−0.867477	−	0.497477i	$-0.834260\pi$
$769$	−14.6472	+	12.2905i	−0.528193	+	0.443207i	0.339284	+	0.940684i	$0.389815\pi$
$770$		0			0
$771$	1.62449	−	2.81369i	0.0585044	−	0.101333i
$772$	−30.4406	+	52.7247i	−1.09558	+	1.89760i
$773$	−1.92649	+	1.61652i	−0.0692910	+	0.0581420i	−0.676775	−	0.736190i	$-0.736623\pi$
$773$	−1.92649	+	1.61652i	−0.0692910	+	0.0581420i	0.607484	+	0.794332i	$0.292179\pi$
$774$	−43.4484	−	36.4575i	−1.56172	−	1.31044i
$775$	−9.36231	+	7.85591i	−0.336304	+	0.282193i
$776$	−42.2854	+	15.3906i	−1.51796	+	0.552491i
$777$		0			0
$778$	8.46286			0.303408
$779$	−33.7447	+	27.4913i	−1.20903	+	0.984978i
$780$	5.26991	−	9.12776i	0.188693	−	0.326826i
$781$	−7.72193	+	2.81055i	−0.276313	+	0.100570i
$782$	−38.1070	−	31.9756i	−1.36270	−	1.14344i
$783$	2.93939	+	16.6701i	0.105045	+	0.595741i
$784$		0			0
$785$	13.9179	+	5.06569i	0.496750	+	0.180802i
$786$	16.3687	−	28.3514i	0.583852	−	1.01126i
$787$	1.36303	+	2.36083i	0.0485866	+	0.0841545i	0.889296	−	0.457332i	$-0.151195\pi$
$787$	1.36303	+	2.36083i	0.0485866	+	0.0841545i	−0.840709	+	0.541487i	$0.817862\pi$
$788$	−6.08306	−	34.4988i	−0.216700	−	1.22897i
$789$	14.7464	+	5.36727i	0.524987	+	0.191080i
$790$	16.7306	−	28.9782i	0.595246	−	1.03100i
$791$		0			0
$792$	17.4982	+	6.36884i	0.621773	+	0.226307i
$793$	11.5334	−	4.19783i	0.409564	−	0.149069i
$794$	31.2254	+	11.3651i	1.10815	+	0.403333i
$795$	0.449493	−	2.54920i	0.0159419	−	0.0904108i
$796$	−20.7101	+	117.453i	−0.734049	+	4.16300i
$797$	−22.0327			−0.780439			−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327			−0.780439			−0.390219	+	0.920722i	$0.627601\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	2.54189	−	14.4158i	0.0898693	−	0.509674i
$801$	−1.08435	+	6.14966i	−0.0383137	+	0.217288i
$802$	40.7203	+	14.8210i	1.43789	+	0.523347i
$803$	−6.82295	+	2.48335i	−0.240777	+	0.0876355i
$804$	10.5175	+	3.82807i	0.370925	+	0.135006i
$805$		0			0
$806$	−13.1998	+	22.8627i	−0.464943	+	0.805306i
$807$	−8.04158	−	2.92690i	−0.283077	−	0.103032i
$808$	2.30113	+	13.0503i	0.0809533	+	0.459109i
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.717633	−	0.696422i	$-0.754774\pi$
$809$	−27.3603	−	47.3893i	−0.961935	−	1.66612i	−0.244302	−	0.969699i	$-0.578559\pi$
$810$	9.12108	−	15.7982i	0.320482	−	0.555091i
$811$	−2.17112	−	0.790224i	−0.0762384	−	0.0277485i	0.303619	−	0.952793i	$-0.401805\pi$
$811$	−2.17112	−	0.790224i	−0.0762384	−	0.0277485i	−0.379858	+	0.925045i	$0.624027\pi$
$812$		0			0
$813$	3.01145	+	17.0788i	0.105616	+	0.598979i
$814$	−9.43629	−	7.91799i	−0.330742	−	0.277525i
$815$	8.01754	−	2.91815i	0.280842	−	0.102218i
$816$	8.40420	−	14.5565i	0.294206	−	0.509579i
$817$	6.04458	+	37.4479i	0.211473	+	1.31014i
$818$	−22.2772			−0.778906
$819$		0			0
$820$	−55.7700	+	20.2986i	−1.94757	+	0.708858i
$821$	0.851167	−	0.714214i	0.0297059	−	0.0249262i	−0.627814	−	0.778364i	$-0.716050\pi$
$821$	0.851167	−	0.714214i	0.0297059	−	0.0249262i	0.657520	+	0.753437i	$0.271606\pi$
$822$	−12.9192	−	10.8405i	−0.450609	−	0.378106i
$823$	15.8170	−	13.2721i	0.551347	−	0.462635i	−0.324050	−	0.946040i	$-0.605045\pi$
$823$	15.8170	−	13.2721i	0.551347	−	0.462635i	0.875397	+	0.483405i	$0.160600\pi$
$824$	38.0886	−	65.9714i	1.32688	−	2.29822i
$825$	−1.23143	+	2.13290i	−0.0428729	+	0.0742580i
$826$		0			0
$827$	27.8116	−	23.3367i	0.967103	−	0.811495i	−0.0149913	−	0.999888i	$-0.504772\pi$
$827$	27.8116	−	23.3367i	0.967103	−	0.811495i	0.982094	+	0.188392i	$0.0603276\pi$
$828$	57.5039			1.99840
$829$	7.14971			0.248320			0.124160	−	0.992262i	$-0.460376\pi$
$829$	7.14971			0.248320			0.124160	+	0.992262i	$0.460376\pi$
$830$	32.1917	−	27.0120i	1.11739	−	0.937600i
$831$	10.1267	−	3.68582i	0.351292	−	0.127860i
$832$	0.772852	+	4.38306i	0.0267938	+	0.151955i
$833$		0			0
$834$	−2.10220	−	1.76395i	−0.0727931	−	0.0610807i
$835$	−9.28177	−	16.0765i	−0.321209	−	0.556350i
$836$	−11.1040	−	19.8934i	−0.384040	−	0.688027i
$837$	6.98070	−	12.0909i	0.241288	−	0.417924i
$838$	3.00758	−	17.0568i	0.103895	−	0.589218i
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.835638	−	0.549280i	$-0.814902\pi$
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.287065	+	0.957911i	$0.592680\pi$
$840$		0			0
$841$	−1.27672	+	7.24065i	−0.0440249	+	0.249678i
$842$	2.12061	+	12.0266i	0.0730812	+	0.414464i
$843$	−12.6560			−0.435896
$844$	17.8045	+	30.8384i	0.612857	+	1.06150i
$845$	7.11334	+	2.58904i	0.244706	+	0.0890658i
$846$	−2.86571	+	2.40462i	−0.0985253	+	0.0826725i
$847$		0			0
$848$	−9.76991	−	16.9220i	−0.335500	−	0.581103i
$849$	1.28194	+	7.27022i	0.0439959	+	0.249513i
$850$	−23.9650	−	20.1090i	−0.821992	−	0.689733i
$851$	−19.5398	−	7.11192i	−0.669817	−	0.243793i
$852$	−15.2986	−	12.8370i	−0.524121	−	0.439790i
$853$	−25.4716	−	21.3732i	−0.872132	−	0.731805i	0.0924142	−	0.995721i	$-0.470542\pi$
$853$	−25.4716	−	21.3732i	−0.872132	−	0.731805i	−0.964546	+	0.263915i	$0.914986\pi$
$854$		0			0
$855$	−14.2781	+	4.96356i	−0.488301	+	0.169750i
$856$	−20.3944	−	35.3241i	−0.697066	−	1.20735i
$857$	−3.65183	+	1.32916i	−0.124744	+	0.0454031i	−0.403638	−	0.914919i	$-0.632254\pi$
$857$	−3.65183	+	1.32916i	−0.124744	+	0.0454031i	0.278894	+	0.960322i	$0.410032\pi$
$858$	−0.923801	+	5.23913i	−0.0315380	+	0.178861i
$859$	−1.26991	+	1.06559i	−0.0433289	+	0.0363573i	−0.664195	−	0.747559i	$-0.731226\pi$
$859$	−1.26991	+	1.06559i	−0.0433289	+	0.0363573i	0.620866	+	0.783917i	$0.286781\pi$
$860$	−8.98158	+	50.9371i	−0.306269	+	1.73694i
$861$		0			0
$862$	1.65048	+	2.85872i	0.0562156	+	0.0973684i
$863$	−52.7187			−1.79457			−0.897284	−	0.441455i	$-0.854463\pi$
$863$	−52.7187			−1.79457			−0.897284	+	0.441455i	$0.854463\pi$
$864$	2.90373	+	16.4679i	0.0987870	+	0.560249i
$865$	−5.90673	−	33.4987i	−0.200835	−	1.13899i
$866$	50.1958			1.70572
$867$	0.636507	+	1.10246i	0.0216169	+	0.0374416i
$868$		0			0
$869$	−2.01795	+	11.4444i	−0.0684543	+	0.388224i
$870$	7.93629	−	6.65934i	0.269065	−	0.225773i
$871$	1.83387	−	10.4004i	0.0621385	−	0.352405i
$872$	54.2418	−	19.7424i	1.83686	−	0.668561i
$873$	−9.48457	−	16.4278i	−0.321004	−	0.555996i
$874$	−42.2918	−	36.5450i	−1.43054	−	1.23615i
$875$		0			0
$876$	−13.5175	−	11.3426i	−0.456715	−	0.383230i
$877$	−16.2324	−	13.6206i	−0.548128	−	0.459934i	0.326179	−	0.945308i	$-0.394239\pi$
$877$	−16.2324	−	13.6206i	−0.548128	−	0.459934i	−0.874307	+	0.485374i	$0.838683\pi$
$878$	82.2486	+	29.9360i	2.77576	+	1.01029i
$879$	−1.94949	−	1.63582i	−0.0657548	−	0.0551748i
$880$	−1.84002	−	10.4353i	−0.0620271	−	0.351773i
$881$	16.0505	+	27.8003i	0.540755	+	0.936616i	0.998861	+	0.0477179i	$0.0151948\pi$
$881$	16.0505	+	27.8003i	0.540755	+	0.936616i	−0.458106	+	0.888898i	$0.651472\pi$
$882$		0			0
$883$	−36.2315	+	30.4018i	−1.21929	+	1.02310i	−0.220425	+	0.975404i	$0.570744\pi$
$883$	−36.2315	+	30.4018i	−1.21929	+	1.02310i	−0.998862	+	0.0476989i	$0.984811\pi$
$884$	−43.6921	−	15.9026i	−1.46953	−	0.534863i
$885$	−1.73055	−	2.99740i	−0.0581719	−	0.100757i
$886$	−43.0711			−1.44700
$887$	−1.83425	−	10.4026i	−0.0615882	−	0.349284i	−0.999993	−	0.00374624i	$-0.998808\pi$
$887$	−1.83425	−	10.4026i	−0.0615882	−	0.349284i	0.938405	−	0.345538i	$-0.112304\pi$
$888$	2.84167	−	16.1159i	0.0953602	−	0.540815i
$889$		0			0
$890$	7.77719	−	2.83067i	0.260692	−	0.0948841i
$891$	−1.10014	+	6.23919i	−0.0368560	+	0.209021i
$892$	−34.1352	+	59.1239i	−1.14293	+	1.97962i
$893$	2.50165	+	0.0362770i	0.0837145	+	0.00121396i
$894$	9.26099	+	16.0405i	0.309734	+	0.536475i
$895$	6.01779	+	5.04952i	0.201153	+	0.168787i
$896$		0			0
$897$	1.55943	+	8.84397i	0.0520679	+	0.295291i
$898$	89.0121	−	32.3978i	2.97037	−	1.08113i
$899$	−13.6775	+	11.4768i	−0.456171	+	0.382773i
$900$	36.1634			1.20545
$901$	−11.4192			−0.380429
$902$	22.9479	−	19.2556i	0.764081	−	0.641141i
$903$		0			0
$904$	4.00088	−	6.92972i	0.133067	−	0.230479i
$905$	9.13610	−	15.8242i	0.303694	−	0.526014i
$906$	13.9795	−	11.7302i	0.464439	−	0.389710i
$907$	32.8790	+	27.5887i	1.09173	+	0.916069i	0.996841	−	0.0794191i	$-0.0253065\pi$
$907$	32.8790	+	27.5887i	1.09173	+	0.916069i	0.0948871	+	0.995488i	$0.469751\pi$
$908$	−33.3632	+	27.9951i	−1.10720	+	0.929050i
$909$	−5.24928	+	1.91058i	−0.174107	+	0.0633699i
$910$		0			0
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$	9.67917	−	16.2171i	0.320509	−	0.537003i
$913$	−7.29726	+	12.6392i	−0.241504	+	0.418297i
$914$	21.6789	−	7.89046i	0.717073	−	0.260993i
$915$	3.04323	+	2.55358i	0.100606	+	0.0844186i
$916$	−15.4119	−	87.4055i	−0.509225	−	2.88796i
$917$		0			0
$918$	33.5822	+	12.2229i	1.10838	+	0.403416i
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	−0.589285	−	0.807925i	$-0.700590\pi$
$919$	12.2788	−	21.2676i	0.405041	−	0.701552i	0.994326	+	0.106373i	$0.0339237\pi$
$920$	−20.8307	−	36.0798i	−0.686767	−	1.18952i
$921$	−2.62671	−	14.8968i	−0.0865529	−	0.490866i
$922$	58.1719	+	21.1729i	1.91579	+	0.697291i
$923$	−9.42190	+	16.3192i	−0.310126	+	0.537154i
$924$		0			0
$925$	−12.2883	−	4.47259i	−0.404038	−	0.147058i
$926$	−0.596571	+	0.217134i	−0.0196046	+	0.00713547i
$927$	30.1755	+	10.9830i	0.991092	+	0.360728i
$928$	3.71348	−	21.0602i	0.121901	−	0.691334i
$929$	3.86840	−	21.9388i	0.126918	−	0.719789i	−0.853232	−	0.521532i	$-0.825361\pi$
$929$	3.86840	−	21.9388i	0.126918	−	0.719789i	0.980150	−	0.198257i	$-0.0635281\pi$
$930$	−8.54488			−0.280198
$931$		0			0
$932$	15.5936			0.510785
$933$	0.392284	−	2.22475i	0.0128428	−	0.0728352i
$934$	6.75449	−	38.3066i	0.221014	−	1.25343i
$935$	−5.81908	−	2.11797i	−0.190304	−	0.0692651i
$936$	40.1257	−	14.6046i	1.31155	−	0.477365i
$937$	−8.97565	−	3.26687i	−0.293222	−	0.106724i	0.191221	−	0.981547i	$-0.438755\pi$
$937$	−8.97565	−	3.26687i	−0.293222	−	0.106724i	−0.484443	+	0.874823i	$0.660978\pi$
$938$		0			0
$939$	−7.47013	+	12.9386i	−0.243779	+	0.422237i
$940$	3.20574	+	1.16679i	0.104560	+	0.0380566i
$941$	9.67664	+	54.8790i	0.315449	+	1.78900i	0.569688	+	0.821861i	$0.307064\pi$
$941$	9.67664	+	54.8790i	0.315449	+	1.78900i	−0.254238	+	0.967142i	$0.581825\pi$
$942$	−9.08424	−	15.7344i	−0.295981	−	0.512654i
$943$	25.2841	−	43.7933i	0.823362	−	1.42610i
$944$	−24.5510	−	8.93582i	−0.799066	−	0.290836i
$945$		0			0
$946$	−4.53343	−	25.7104i	−0.147395	−	0.835916i
$947$	−20.7160	−	17.3828i	−0.673180	−	0.564865i	0.240825	−	0.970569i	$-0.422582\pi$
$947$	−20.7160	−	17.3828i	−0.673180	−	0.564865i	−0.914005	+	0.405704i	$0.867026\pi$
$948$	−26.5390	+	9.65939i	−0.861945	+	0.313722i
$949$	−8.32501	+	14.4193i	−0.270241	+	0.468071i
$950$	−26.5967	−	22.9826i	−0.862912	−	0.745656i
$951$	17.0490			0.552852
$952$		0			0
$953$	−21.7361	+	7.91128i	−0.704100	+	0.256272i	−0.669161	−	0.743118i	$-0.733346\pi$
$953$	−21.7361	+	7.91128i	−0.704100	+	0.256272i	−0.0349398	+	0.999389i	$0.511124\pi$
$954$	14.6964	−	12.3317i	0.475814	−	0.399255i
$955$	−10.6141	−	8.90625i	−0.343463	−	0.288199i
$956$	40.4634	−	33.9528i	1.30868	−	1.09811i
$957$	−1.79901	+	3.11598i	−0.0581538	+	0.100725i
$958$	0.910597	−	1.57720i	0.0294200	−	0.0509570i
$959$		0			0
$960$	−1.10354	+	0.925981i	−0.0356166	+	0.0298859i
$961$	−16.2736			−0.524956
$962$	−28.2472			−0.910727
$963$	13.1716	−	11.0523i	0.424449	−	0.356155i
$964$	53.4830	−	19.4662i	1.72257	−	0.626965i
$965$	3.22874	+	18.3111i	0.103937	+	0.589455i
$966$		0			0
$967$	29.9026	+	25.0913i	0.961603	+	0.806881i	0.981213	−	0.192927i	$-0.0617980\pi$
$967$	29.9026	+	25.0913i	0.961603	+	0.806881i	−0.0196101	+	0.999808i	$0.506242\pi$
$968$	−29.2977	−	50.7451i	−0.941664	−	1.63101i
$969$	−5.37939	−	9.63744i	−0.172811	−	0.309599i
$970$	−12.5706	+	21.7729i	−0.403617	+	0.699085i
$971$	7.15476	−	40.5767i	0.229607	−	1.30217i	−0.624071	−	0.781367i	$-0.714523\pi$
$971$	7.15476	−	40.5767i	0.229607	−	1.30217i	0.853679	−	0.520800i	$-0.174366\pi$
$972$	−59.7135	+	21.7339i	−1.91531	+	0.697117i
$973$		0			0
$974$	−5.16503	+	29.2923i	−0.165498	+	0.938587i
$975$	0.980704	+	5.56185i	0.0314077	+	0.178122i
$976$	29.9881			0.959897
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	0.628110	−	0.778125i	$-0.283829\pi$
$977$	−11.2469	−	19.4802i	−0.359821	−	0.623227i	−0.987931	+	0.154897i	$0.950495\pi$
$978$	−9.83497	−	3.57964i	−0.314488	−	0.114464i
$979$	−2.20187	+	1.84759i	−0.0703720	+	0.0590491i
$980$		0			0
$981$	12.1664	+	21.0728i	0.388442	+	0.672802i
$982$	−0.0390581	−	0.221510i	−0.00124640	−	0.00706866i
$983$	34.1243	+	28.6337i	1.08840	+	0.913273i	0.996591	−	0.0825035i	$-0.0262916\pi$
$983$	34.1243	+	28.6337i	1.08840	+	0.913273i	0.0918061	+	0.995777i	$0.470736\pi$
$984$	37.3965	+	13.6112i	1.19216	+	0.433910i
$985$	−8.19569	−	6.87700i	−0.261136	−	0.219119i
$986$	−35.0107	−	29.3775i	−1.11497	−	0.935570i
$987$		0			0
$988$	−48.8285	−	18.5782i	−1.55344	−	0.591052i
$989$	−22.0351	−	38.1659i	−0.700675	−	1.21360i
$990$	9.77631	−	3.55829i	0.310712	−	0.113090i
$991$	−7.87140	+	44.6409i	−0.250043	+	1.41807i	0.558440	+	0.829545i	$0.311400\pi$
$991$	−7.87140	+	44.6409i	−0.250043	+	1.41807i	−0.808483	+	0.588520i	$0.799711\pi$
$992$	−13.5116	+	11.3376i	−0.428994	+	0.359969i
$993$	2.15853	−	12.2416i	0.0684988	−	0.388476i
$994$		0			0
$995$	18.2121	+	31.5443i	0.577363	+	1.00002i
$996$	−35.4688			−1.12387
$997$	1.82177	+	10.3317i	0.0576959	+	0.327210i	0.999971	−	0.00763028i	$-0.00242882\pi$
$997$	1.82177	+	10.3317i	0.0576959	+	0.327210i	−0.942275	+	0.334840i	$0.891318\pi$
$998$	−6.45929	−	36.6325i	−0.204465	−	1.15958i
$999$	14.9385			0.472634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.v.a.263.1		6
7.2	even	3		931.2.x.b.814.1		6
7.3	odd	6		19.2.e.a.16.1	yes	6
7.4	even	3		931.2.w.a.491.1		6
7.5	odd	6		931.2.x.a.814.1		6
7.6	odd	2		931.2.v.b.263.1		6
19.6	even	9		931.2.x.b.557.1		6
21.17	even	6		171.2.u.c.73.1		6
28.3	even	6		304.2.u.b.225.1		6
35.3	even	12		475.2.u.a.149.1		12
35.17	even	12		475.2.u.a.149.2		12
35.24	odd	6		475.2.l.a.301.1		6
133.3	even	18		361.2.c.h.68.1		6
133.6	odd	18		931.2.x.a.557.1		6
133.10	even	18		361.2.e.a.99.1		6
133.17	odd	18		361.2.c.i.292.3		6
133.24	odd	18		361.2.a.g.1.1		3
133.25	even	9		931.2.w.a.785.1		6
133.31	even	6		361.2.e.a.62.1		6
133.44	even	9	inner	931.2.v.a.177.1		6
133.45	odd	6		361.2.e.g.62.1		6
133.52	even	18		361.2.a.h.1.3		3
133.59	even	18		361.2.c.h.292.1		6
133.66	odd	18		361.2.e.g.99.1		6
133.73	odd	18		361.2.c.i.68.3		6
133.80	odd	18		361.2.e.f.28.1		6
133.82	odd	18		931.2.v.b.177.1		6
133.87	odd	6		361.2.e.f.245.1		6
133.94	even	6		361.2.e.h.54.1		6
133.101	odd	18		19.2.e.a.6.1	✓	6
133.108	even	18		361.2.e.h.234.1		6
133.122	even	6		361.2.e.b.245.1		6
133.129	even	18		361.2.e.b.28.1		6
399.101	even	18		171.2.u.c.82.1		6
399.185	odd	18		3249.2.a.s.1.1		3
399.290	even	18		3249.2.a.z.1.3		3
532.367	even	18		304.2.u.b.177.1		6
532.423	even	18		5776.2.a.br.1.2		3
532.451	odd	18		5776.2.a.bi.1.2		3
665.24	odd	18		9025.2.a.bd.1.3		3
665.234	odd	18		475.2.l.a.101.1		6
665.367	even	36		475.2.u.a.424.1		12
665.584	even	18		9025.2.a.x.1.1		3
665.633	even	36		475.2.u.a.424.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	133.101	odd	18
19.2.e.a.16.1	yes	6	7.3	odd	6
171.2.u.c.73.1		6	21.17	even	6
171.2.u.c.82.1		6	399.101	even	18
304.2.u.b.177.1		6	532.367	even	18
304.2.u.b.225.1		6	28.3	even	6
361.2.a.g.1.1		3	133.24	odd	18
361.2.a.h.1.3		3	133.52	even	18
361.2.c.h.68.1		6	133.3	even	18
361.2.c.h.292.1		6	133.59	even	18
361.2.c.i.68.3		6	133.73	odd	18
361.2.c.i.292.3		6	133.17	odd	18
361.2.e.a.62.1		6	133.31	even	6
361.2.e.a.99.1		6	133.10	even	18
361.2.e.b.28.1		6	133.129	even	18
361.2.e.b.245.1		6	133.122	even	6
361.2.e.f.28.1		6	133.80	odd	18
361.2.e.f.245.1		6	133.87	odd	6
361.2.e.g.62.1		6	133.45	odd	6
361.2.e.g.99.1		6	133.66	odd	18
361.2.e.h.54.1		6	133.94	even	6
361.2.e.h.234.1		6	133.108	even	18
475.2.l.a.101.1		6	665.234	odd	18
475.2.l.a.301.1		6	35.24	odd	6
475.2.u.a.149.1		12	35.3	even	12
475.2.u.a.149.2		12	35.17	even	12
475.2.u.a.424.1		12	665.367	even	36
475.2.u.a.424.2		12	665.633	even	36
931.2.v.a.177.1		6	133.44	even	9	inner
931.2.v.a.263.1		6	1.1	even	1	trivial
931.2.v.b.177.1		6	133.82	odd	18
931.2.v.b.263.1		6	7.6	odd	2
931.2.w.a.491.1		6	7.4	even	3
931.2.w.a.785.1		6	133.25	even	9
931.2.x.a.557.1		6	133.6	odd	18
931.2.x.a.814.1		6	7.5	odd	6
931.2.x.b.557.1		6	19.6	even	9
931.2.x.b.814.1		6	7.2	even	3
3249.2.a.s.1.1		3	399.185	odd	18
3249.2.a.z.1.3		3	399.290	even	18
5776.2.a.bi.1.2		3	532.451	odd	18
5776.2.a.br.1.2		3	532.423	even	18
9025.2.a.x.1.1		3	665.584	even	18
9025.2.a.bd.1.3		3	665.24	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 + 2.49362i) q^{2} +(0.113341 - 0.642788i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(-1.26604 + 0.460802i) q^{5} +(1.55303 + 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(2.41875 + 0.880352i) q^{9} +O(q^{10})\)	\(q+(-0.439693 + 2.49362i) q^{2} +(0.113341 - 0.642788i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(-1.26604 + 0.460802i) q^{5} +(1.55303 + 0.565258i) q^{6} +(3.05303 - 5.28801i) q^{8} +(2.41875 + 0.880352i) q^{9} +(-0.592396 - 3.35965i) q^{10} +(0.592396 + 1.02606i) q^{11} +(-1.43969 + 2.49362i) q^{12} +(2.55303 + 0.929228i) q^{13} +(0.152704 + 0.866025i) q^{15} +(5.08512 + 4.26692i) q^{16} +(3.64543 - 1.32683i) q^{17} +(-3.25877 + 5.64436i) q^{18} +(4.11721 - 1.43128i) q^{19} +5.94356 q^{20} +(-2.81908 + 1.02606i) q^{22} +(-3.87939 + 3.25519i) q^{23} +(-3.05303 - 2.56180i) q^{24} +(-2.43969 + 2.04715i) q^{25} +(-3.43969 + 5.95772i) q^{26} +(1.81908 - 3.15074i) q^{27} +(-3.56418 + 2.99070i) q^{29} -2.22668 q^{30} +3.83750 q^{31} +(-3.52094 + 2.95442i) q^{32} +(0.726682 - 0.264490i) q^{33} +(1.70574 + 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} +(2.05303 + 3.55596i) q^{37} +(1.75877 + 10.8961i) q^{38} +(0.886659 - 1.53574i) q^{39} +(-1.42855 + 8.10170i) q^{40} +(-9.38326 + 3.41523i) q^{41} +(-1.51114 + 8.57013i) q^{43} +(-0.907604 - 5.14728i) q^{44} -3.46791 q^{45} +(-6.41147 - 11.1050i) q^{46} +(0.539363 + 0.196312i) q^{47} +(3.31908 - 2.78504i) q^{48} +(-4.03209 - 6.98378i) q^{50} +(-0.439693 - 2.49362i) q^{51} +(-9.18139 - 7.70410i) q^{52} +(-2.76604 - 1.00676i) q^{53} +(7.05690 + 5.92145i) q^{54} +(-1.22281 - 1.02606i) q^{55} +(-0.453363 - 2.80872i) q^{57} +(-5.89053 - 10.2027i) q^{58} +(-3.69846 + 1.34613i) q^{59} +(0.673648 - 3.82045i) q^{60} +(3.46064 - 2.90382i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(0.819078 + 1.41868i) q^{64} -3.66044 q^{65} +(0.340022 + 1.92836i) q^{66} +(-0.674992 - 3.82807i) q^{67} -17.1138 q^{68} +(1.65270 + 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(12.0398 - 10.1026i) q^{72} +(-1.06418 + 6.03525i) q^{73} +(-9.76991 + 3.55596i) q^{74} +(1.03936 + 1.80023i) q^{75} +(-19.2271 - 0.278817i) q^{76} +(3.43969 + 2.88624i) q^{78} +(7.51367 + 6.30472i) q^{79} +(-8.40420 - 3.05888i) q^{80} +(4.09627 + 3.43718i) q^{81} +(-4.39053 - 24.8999i) q^{82} +(6.15910 + 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(-20.7062 - 7.53644i) q^{86} +(1.51842 + 2.62998i) q^{87} +7.23442 q^{88} +(0.421274 + 2.38917i) q^{89} +(1.52481 - 8.64766i) q^{90} +(20.9932 - 7.64090i) q^{92} +(0.434945 - 2.46669i) q^{93} +(-0.726682 + 1.25865i) q^{94} +(-4.55303 + 3.70929i) q^{95} +(1.50000 + 2.59808i) q^{96} +(-5.64543 - 4.73708i) q^{97} +(0.529563 + 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9} - 3 q^{12} + 3 q^{13} + 3 q^{15} + 9 q^{16} + 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} - 12 q^{23} - 6 q^{24} - 9 q^{25} - 15 q^{26} - 6 q^{27} - 3 q^{29} + 18 q^{31} - 18 q^{32} - 9 q^{33} - 24 q^{36} - 12 q^{38} + 12 q^{39} - 9 q^{40} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 30 q^{45} - 18 q^{46} + 12 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{54} - 18 q^{55} + 24 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} + 24 q^{65} - 18 q^{66} + 6 q^{67} - 30 q^{68} + 12 q^{69} - 6 q^{71} + 15 q^{72} + 12 q^{73} - 30 q^{74} + 15 q^{75} - 36 q^{76} + 15 q^{78} + 24 q^{79} - 12 q^{80} - 3 q^{81} - 9 q^{82} - 48 q^{86} + 21 q^{87} - 18 q^{88} - 15 q^{89} - 18 q^{90} + 42 q^{92} - 36 q^{93} + 9 q^{94} - 15 q^{95} + 9 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9 - 3 * q^12 + 3 * q^13 + 3 * q^15 + 9 * q^16 + 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 - 12 * q^23 - 6 * q^24 - 9 * q^25 - 15 * q^26 - 6 * q^27 - 3 * q^29 + 18 * q^31 - 18 * q^32 - 9 * q^33 - 24 * q^36 - 12 * q^38 + 12 * q^39 - 9 * q^40 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 30 * q^45 - 18 * q^46 + 12 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^54 - 18 * q^55 + 24 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 + 24 * q^65 - 18 * q^66 + 6 * q^67 - 30 * q^68 + 12 * q^69 - 6 * q^71 + 15 * q^72 + 12 * q^73 - 30 * q^74 + 15 * q^75 - 36 * q^76 + 15 * q^78 + 24 * q^79 - 12 * q^80 - 3 * q^81 - 9 * q^82 - 48 * q^86 + 21 * q^87 - 18 * q^88 - 15 * q^89 - 18 * q^90 + 42 * q^92 - 36 * q^93 + 9 * q^94 - 15 * q^95 + 9 * q^96 - 18 * q^97 + 9 * q^99

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